Extrema, Increasing/Decreasing Functions and Concavity Review

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

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

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

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

 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

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-BF.B.4A

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

How many extrema are in the picture?

• 2
• 3
• 4
• 5

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

On what interval(s) is the function
y = x^3 + 6x^2
concave down?

• (-∞,-4)
• (-∞,-2)
• (-2,∞)
• (0,∞)