Calculus 1st and 2nd derivative Quiz

An absolute maximum must occur at a critical point or at an endpoint.

• True
• False

A critical number, c, or a function f is a number in the domain of f such that:

• f'(c) = 0
• f'(c) is undefined
• f'(c) = o or f'(c) is undefined
• None of the above

If c is a critical number then f(c) is either a local maximum or a local minimum

• True
• False

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

Tags

CCSS.HSA.APR.B.3

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)
• (0,1)
• (-∞,-1) and (1,∞)
• (0,1) and (-1,0)

Tags

CCSS.HSG.SRT.C.8

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

• None
• x = 0
• x = 0, 2
• x = -2, 0, 2

Tags

CCSS.HSF-IF.C.7D

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

• None
• x = 0
• x = 0, 2
• x = -2, 0, 2

Tags

CCSS.HSF-IF.C.7D

What is the interval(s) where f(x) is concave down for f(x) = 2(x)^1/5 + 3?

• (-∞,0)
• (0,∞)
• None
• (-∞, ∞)

If given a graph of f'(x) how do you determine the values of x at which f (x) has a relative maximum?

• f'(x) has a change in values from positive to negative
• f'(x) has a change in values of y from negative to positive
• Value of f'(x) = 0
• Value of f'(x) DNE

If given f'(x) how do you find the values of x at which f(x) has a point of inflection?

• f"(critical point)
• f'(x) DNE
• f'(x) = 0
• The max or min of f'(x)