If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

Answers

Answer 1

Answer:

[tex]f'( x ) = \frac{f(b) - f(a)}{b - a} \\ = \frac{f(6) -f(a)}{6 - 1} \\ 3\leqslant \frac{f(6) - 10}{5} \\ 15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25[/tex]

Answer 2

Answer:

25

Step-by-step explanation:

Our "best" case is when [tex]f'(x) = 3[/tex] everywhere - if it changes it means [tex]f(x)[/tex] will grow faster. But if [tex]f'(x)[/tex] is constant, it means [tex]f(x)[/tex] is the straight line [tex] y-10 = 3 (x-1) [tex], which passes through the point (6, 25)


Related Questions

Your mother drives 60 minutes at a constant speed of 40 miles per hour. She then speeds up, and drives for another 30 minutes at a constant speed of 70 miles per hour. How many miles does your mother travel all together? How long did the trip take?

Answers

Answer: written below

Step-by-step explanation:

1 hour time 40 miles/ hour =1*40=40miles

0.5 *70=0.5*70=35 miles

40+35=75 miles

60 minutes+30 minutes= 90 minutes or 1 1/2hours

The temperature at 10:00 a.m was -3 and increased 2.25 each hour for the next 5 hours.What was the temperature at 3:00pm?

Answers

9514 1404 393

Answer:

  8.25°

Step-by-step explanation:

The increase over 5 hours was ...

  (5 h) × (2.25 °/h) = 11.25°

When that is added to the starting value, the ending value is ...

  -3° +11.25° = 8.25°

The temperature at 3:00 pm was 8.25°.

2x=20−2

Value of x!!!​

Answers

Answer:

[tex]\sf\longmapsto \: x = 9[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: 2x = 20 - 2[/tex]

[tex]\sf\longmapsto \: 2x = 18[/tex]

[tex]\sf\longmapsto \: x = \frac{18}{2} [/tex]

[tex]\sf\longmapsto \: x = 9[/tex]

Hello there! :)

2x=20-2

2x=18

Divide both sides by 2 to isolate x:

x=9

Hope this helps!

#HaveAnAmazingDay

[tex]GraceRosalia[/tex]

Helpp need it now


9.) Find the N' .

1.) {j , u , d , g}
2.) {m , n , t , a , l}
3.) {j , u , d , g , e}
4.) {m , e , n , t , a , l}

10.) Find the N U I.

1.) {m , n , t , a , l}
2.) {j , u , d , g , e}
3.) {m , e , n , t , a , l}
4.) {j , u , d , g , m , e , n , t , a , l}

Answers

Answer:

8.) ans {e}

9.) ans {j, u, d, g}

10.) ans {j, u, d, g, m, e, n, t, a, l}

In a multiple choice test, a candidate gets 3 marks for a correct answer and one mark is deducted for an incorrect answer. If Ayobi answers all 30 questions and scores 30 marks, how many questions did
she get wrong?

Reason too

Answers

Answer:

30/3 = 10

Step-by-step explanation:

Divide 30 by 3 to get your answer which is going to be 10

30 ÷ 3= 10

Since you get 3 marks each answer. You will divide 30 by 3. Which is 10.

Indhu has 150 stamps and Clarissa has 78 stamps. How many stamps must Indhu give Clarissa so that they will have the same number of stamps?​

Answers

Answer:

36 stamps

Step-by-step explanation:

150+78=228

228/2=114

150-114=36

On Sunday a local hamburger shop sold a combined total of 231 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the amount of hamburgers sold. How many hamburgers were sold on Sunday?

Answers

Answer: 77 hamburgers

Step-by-step explanation:

You can write an equation for this problem

x= hamburgers

2x= cheeseburgers

x+2x=231

3x=231

x=77

please answer this question above​

Answers

Answer:

2

Step-by-step explanation:

whatever number to the zero power equals 1

for example

192 to the zero power equals 1

7,000332 to the zero power equals 1

x to the zero power equals 1

so 1+1+1+1=4

(4)^1/2

2

i dk who made that rule its a little confusing but whatever

Brainliest?

can anyone heelp me pls

Answers

Lotion - liquid

Suspension- semisolid

Capsule- Solid

Hope this helps :)

9. Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7,0).

Answers

Answer:

[tex]x = \frac{1}{28} y^{2}[/tex]

Step-by-step explanation:

parabola equation with vertex (0 , 0) and focus length |f| = 7

4*f*(x - h) = (y - k)²

4*7*(x-0)=(y-0)²

28x = y²

[tex]x = \frac{1}{28} y^{2}[/tex]

I WILL MARK BRAINLIST

Answers

It’s the third choice

Find the Perimeter of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.

Answers

Step-by-step explanation:

the perimeter = 2 ×15 + (π×d)

= 30 + (3.14 ×10)

= 30 + 31.4

= 61.4

At the bus station, buses depart a rate if 3 every 10 minutes. At the rate, how many buses would you expect to depart in one one hour?

A. 6
B. 15
C. 18
D. 30

Answers

Answer:

C.18

Step-by-step explanation:

at the rate 18 buses would have departed

The answer is 18 because if 3 buses depart at a rate of 10 minutes just multiply 10 minutes by 6 and that’ll equal an hour then multiply the 3 x 6 and that’s equals 18 which is the answer

Please answer the question step by step!

Answers

Answer:

Step-by-step explanation:

See the figure below.

This is how you graph directly from the equation in the slope-intercept form (y = mx + b) without having to create a table of x and y values.

The equation is

y = -2/3 x + 1

Compare it with

y = mx + b

b = 1

The y-intercept is 1, so mark 1 on the y-axis. (You already did.)

I placed a black dot there.

The slope is m.

m = -2/3

slope = m = rise/run

A slope of -2/3 can be though of as -2 rise and 3 run. That means start from the y-intercept, and go -2 in y (a rise of 2 down) and 3 in x (a run 3 right). Point graphed in red.

Mathematically, -2/3 is the same as 2/(-3), so starting again from the y-intercept, this slope can also be though of as rise of 2 in y (a rise of 2 up) and a run of -3 in x (a run of 3 left). Point graphed in green.

The line is graphed in blue.

........................

Help or don’t if so thank you

Answers

Answer: 12.60 per CD

Step-by-step explanation:

Tax 0.80 * 3 = 2.40

40.20 - 2.40 = 37.80

37.8 / 3 = 12.60

What is the distance between point C (3.5,6) and Point A (4.8, 6)​

Answers

Answer:

-1/3 and 0

Step-by-step explanation:

3.5-4.8=-1.3

6-6=0

I'm possibly wrong, but I need the points, and brainiest so, sorry if it is wrong.

Assume that y varies inversely as x. If
Y
y = 10 when
=
x = 4, what is the value for y when
x = 6?

Answers

Answer:

x=5

Explanation:

y∝1x∴y=k⋅1x∴x⋅y=k;

When x=4;y=10∴4⋅10=kork=40.

So variation equation is x⋅y=40

When y=8;x=408=5∴x=5 [Ans]

Step-by-step explanation:

not surre

Answer:

6.67

Step-by-step explanation:

10=4

y=6

10×4/6

The graph shows the motion of a car on a highway.

Which statement describing the motion of the car is best supported by the graph?

Answers

Answer:

you didnt give the options .. but its going to be the one saying something like its staying the same speed.

What is the product of 246 and 176?​

Answers

Answer:

43296

Step-by-step explanation:

Answer: 43296

Step-by-step explanation:

If you multiply 246 and 176, you get 43296.

Mrs. Trip landed at Boston Logan airport and exchanged 700 Euro for $875 at a currency exchange store. Then she realized that she would need more cash and exchanged 400 Euro more. How many dollars did she receive for the second transaction?

Answers

Answer:

$500

Step-by-step explanation:

find the ratio

875/700=5/4

apply the ratio

5/4*400=500

It takes 12 hours to fill a pool with the inlet pipe. It can be emptied in 15 hours with the outlet pipe. If the pool is 1/2 full to begin with, how long will it take to fill it from there if both pipes are open?

Answers

6 should be right answer to your problem

Answer:

12x15=100

Step-by-step explanation:

Its times because I know it

the general solution of sinx + cosx =√2 is..??​

Answers

The answer is A. x= [tex]\pi[/tex]/4 +2[tex]\pi[/tex]n

Answer:

the general solution has answer

2nπ+π/4

Find x. Round your answer to the nearest tenth of a degree.

Answers

Answer:

x = 50.5°

Step-by-step explanation:

Use SOH CAH TOA... Since the adjacent and hypotenuse are given, you must use cosine.

cos(x) = 14/22

cos^-1 (14/22) = 50.5°

what 21.807-10.739=?​

Answers

Answer:

2.428 is the answer....

Triangles PQR and XYZ are similar. What is the length of XZ?

Answers

3x3x3x3x3= you do the math

Create a proportion from each set of numbers. Only use 4 numbers from each set.

Answers

Step-by-step explanation:

Approach: If four numbers a, b, c and d are in proportion then a:b = c:d. The solution is to sort the four numbers and pair up the first 2 together and the last 2 together and check their ratios this is because, in order for them to be in proportion, the product of means has to be equal to the product of extremes.

I NEED A 100% ACCURATE ANSWER FOR THIS ASAP NO LINKS !!!
Solve the following: 7y−20=3y+12
1: y= 3.2
2: y=8
2: y= -8
4: y= 28

Answers

Answer:

y=8

Step-by-step explanation:

7y-20=3y+12

7y-3y=12+20

4y/4=32/4

y=8

Answer:

7y-3y=12+20

4y=32

y=8

that's it. i don't know why I need 20 max character to submit

Each side of a square calendar is 19 inches long. What is the calendar's perimeter?

Answers

Answer:

a square has 4 sides each of those sides is 19in long perimeter is all around the square so you would add 19+19+19+19=79in

Answer: What is 76'' perimeter

19" side

P=4a=4·19=76in

Please allow me to know if my answer helped you by clicking thank you, rating or brainly.

Miss Hawaii

{-13,-2,9,20,31,…} which term in this sequence is 306

Answers

Given :-

-13,-2,9,20,31 . . . . .

To find :-

which term in this sequence is 306 .

Solution :-

Common difference ,

d = 31 - 20 d = 11

As we know that ,

Tⁿ = a + (n-1)d 306 = -13 + (n-1)11306+13 = (n-1)11319/11 = n-129 = n -1 n = 30

Answer:

30th

Step-by-step explanation:

There is a common difference between consecutive terms, that is

- 2 - (- 13) = 9 - (- 2) = 20 - 9 = 31 - 20 = 11

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 13 and d = 11 , then

[tex]a_{n}[/tex] = - 13 + 11(n - 1) = - 13 + 11n - 11 = 11n - 24 ← equate to 306

11n - 24 = 306 ( add 24 to both sides )

11n = 330 ( divide both sides by 11 )

n = 30

The 30th term is 306

I NEED HELP PLEASE!!!

Passing through (7,-2) and perpendicular to the line whose equation is y=1/2x+2

Point slope form=

Slope-intercept form=

Answers

Answer:

yyou slope intrecept is already there

Step-by-step explanation:

2+2=4

Answer:

9x+3y=36

Step-by-step explanation:

boom

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