IB2 10-2 Concavity & the Second Derivative

The derivative of f at a is the instantaneous rate of

change of f at the point a.

• True

• False

If f′′ > 0 on an interval, then f′ > 0 on that interval.

• True

• False

There is a function with f′′ = 0 everywhere.

• True

• False

• True

• False

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

When f'(x) changes from negative to positive, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

When f'(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

What will be true at an inflection point?  (select the best answer)

• f(x)=0
• f'(x)=0
• f''(x)=0
• The function is undefined

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• increasing
• decreasing
• concave up
• concave down