f, f', f" Quiz (5.3-5.4)

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

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

• It's positive

• It's negative

• It's zero

• Cannot be determined

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

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

When you check for sign changes at the critical numbers of a function, you are using the

• IVT

• MVT

• 1st Derivative Test

• 2nd Derivative Test

Which of the following could be the graph of f ' , the derivative of f ?

• 
• 
• 
• 
• 

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

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

• It's positive

• It's negative

• It's zero

Find the x values where the relative minimum(s) occur for f(x)=3x⁴-2x³-9x²

• -1

• 0

• 1.5

• -1 and 1.5