Function Analysis, MVT, and extremas

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

Tags

CCSS.HSF.IF.B.4

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

• increasing
• decreasing
• concave up
• concave down

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

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

f''(x) is pictured. Over which interval is f(x) concave up? (Be careful - this is a second derivative graph!)

• (-infinity, 3)

• (-5, -1)

• nowhere

• (0, 4)

f''(x) is pictured. Which x values are inflection points of f(x)? (Be careful - this is a second derivative graph!)

• x=-5 and -1

• x=-3

• x=4

• no inflection points