Calculus Unit 5 quiz

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

Tags

CCSS.HSA.APR.B.3

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing
• increasing
• concave up
• concave down

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.HSF.IF.C.7

Given a function g(x), if g''(x)=0 for a certain value of x, then g(x) has _________ at x.

• an inflection point
• a maximum
• a minimum
• a critical point

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point
• a critical point
• a minimum
• a maximum

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.IF.B.6

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

f(x) is pictured. Over what interval is f(x) apparently decreasing?

• (infinity, 0)
• (-infinity, 0)
• (-infinity, infinity)
• (0, infinity)

Tags

CCSS.HSF-IF.C.7A

f(x) is pictured. Over which interval is f(x) apparently concave up?

• (0, infinity)
• (-infinity, infinity)
• (-infinity, 0)
• nowhere

Tags

CCSS.HSF.IF.C.7