function analysis/ optimization

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.B.4

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

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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

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

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

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

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