First Derivative Test for Local Extrema

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

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

When the first derivative is positive, the function is always

• Increasing

• Decreasing

• Concave up

• Concave down

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

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

When f'(x) changes from negative to positive, 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

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

• increasing
• decreasing
• concave up
• concave down

What is the absolute min of this function?

• 0
• -7.5
• -7.5 and 0
• 4

True or false: all critical points are extrema

• True

• False

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points