Free Printable Unit 5 Review questions

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Unit 5 Review questions

Total questions: 18

Worksheet time: 33mins

Name

Class

Date

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

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

f(x) = x³ + 6x² + 9x + 3 on [-4,0]

-4

-1

Which intervals of the graph are increasing?

f(x) = 2x⁴- 4x² + 1

(-1,0)

(0,1)

(-∞,-1) and (1,∞)

(-1,0) and (1, $\infty$ )

Where is the point of inflection for the function $f\left(x\right)=x^3+6x^2$ ?

$x=0$

$x=-4$

$x=-2$

$x=2$

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

increasing

decreasing

concave up

concave down

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

increasing

decreasing

concave up

concave down

When the first derivative is positive, the function is always

Increasing

Decreasing

Concave up

Concave down

For what value of c is the Rolle's theorem applicable on the given function f(x) = x²-5x+4 [1,4]

c = 7/2

c = 5/2

c = 3/2

c = 9/2

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

an inflection point

a critical point

a relative maximum

a relative minimum

10.

Given this graph of f'(x), match the correct interval to what is happening with the function f(x).

[-3,-2] and [0, 3]

f(x) is increasing

(-1,1) and (2,3)

f(x) is concave up

x=-2

f(x) has a local max

(-3,-1) and (1,2)

f(x) is concave down

x=-1, 1, 2

f(x) has a point of inflection

11.

A function is increasing when f'(x) (a)

A function has a local maximum when f'(x) (b)

A function has a point of inflection when f'(x) (c)

A function is concave up when f'(x) (d)

Choose from the below words

changes from positive to negative

changes from negative to positive

is positive

is negative

has a local extrema

is decreasing

is concave up

is concave down.

is increasing

12.

Given the function g'(x), Make each statement TRUE!

g(x) has a (a) at x = 0,2,3

because g'(x) (b)

Choose from the below words

point of inflection

relative max

relative min

has relative extrema

is increasing

is decreasing

has a slope of 0

13.

$f\left(8\right)$ is a:

relative max

relative min

neither

14.

$f\left(x\right)$ is ____________ on the interval $\left(-3,-1\right)$

increasing

decreasing

positive

negative

15.

Order the derivatives of each point on the graph from least to greatest.

ABC

BCA

CBA

BAC

16.

Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?

x=-1 and x=4

x=-3

x=1

x=3

17.

Does mean value theorem apply for f over [-1,2]

YES

18.

On what interval(s) is the function y=x³ + 6x²

concave down?

(-∞,-4)

(-∞,-2)

(-2,∞)

(0,∞)

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Unit 5 Review questions

Total questions: 18

Worksheet time: 33mins

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