First & Second Derivative Tests

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

Tags

CCSS.HSF.IF.B.4

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

• increasing
• decreasing
• concave up
• concave down

 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

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the relative max of this function?

• 5
• infinity
• DNE
• 2.5

What relative minima does this function have?

• 0
• 0 and 4
• -7.5 and 0
• 2.5

Tags

CCSS.HSA.REI.D.10

What is the absolute min of this function?

• 0
• -7.5
• -7.5 and 0
• 4

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.LE.B.5

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

• increasing
• decreasing
• concave up
• concave down