Extrema and MVT

Extrema and MVT

11th Grade - University

16 Qs

quiz-placeholder

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Extrema and MVT

Extrema and MVT

Assessment

Quiz

Mathematics

11th Grade - University

Practice Problem

Medium

CCSS
HSA.REI.D.11, HSA.APR.A.1

Standards-aligned

Created by

John Getz

Used 29+ times

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16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Given that  f(x)f\left(x\right)  is a continuous function, if  f(x)<0f'\left(x\right)<0  over a certain interval, then  f(x)f\left(x\right)  is _________ over that interval.


decreasing

increasing

concave up

concave down

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Given that  f(x)f\left(x\right)  is a continuous function, if  f(x)>0f'\left(x\right)>0  over an interval, then  f(x)f\left(x\right)  is __________ over that interval.


increasing

decreasing

concave up

concave down

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Media Image

Use the sign chart for f'(x).
There is(are) ...

a local maximum at x = -2.
a local maximum at x = 4.
local maxima at x = -2 and x = 4.
no extrema.

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which value is guaranteed by the MVT for the function given: f(x) = x2 - 6x + 8 on [0,3]

f(c) = 10

f(c) = 4

f ' (c) = -3

f ' (c) = 7/3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

Use the sign chart for f'(x).  There is(are) ...

a local maximum at x = -2.
a local minimum at
x = -2 and a local maximum at x = 4.
a local maximum at
x = -2 and a local minimum at x = 4.
no extrema.

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find all values of c that satisfy the MVT for the function on the given interval


f(x) = -x2 + 8x - 17 on [2,6]

c = 2

c = 3

c = 4

c = 6

Tags

CCSS.HSA.REI.D.11

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the absolute maximum for the function on the given interval.


f(x) = x3 + 6x2 + 9x + 3 on [-4,0]

-4

-1

0

3

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