Derivative Graphs

Which one of the following statements is always true?

• When a graph is increasing, its derivative is negative.

• When a graph is decreasing, so is its derivative.

• When a graph is decreasing, its derivative is negative.

• When a graph is increasing, so is its derivative.

Tags

CCSS.HSF.IF.B.4

f(x) is a polynomial function. Which one of the following statements is FALSE?

• f(x) has a derivative of zero when the graph of f(x) has a relative min or max.

• If the derivative of f(x) changes from positive to negative at some point, then the graph of f(x) has a relative minimum at that point.

• If the derivative of f(x) is always positive, then the graph of f(x) has no relative extrema.

• If the graph of f(x) is always increasing, then the derivative of f(x) is never negative.

Tags

CCSS.HSF.IF.C.7

7.

• (A)

• (B)

• (C)

• (D)

• A

• B

• C

• D

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing

Which graph is the derivative of the top graph?

• A
• B
• C
• D

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

f' is given, which could be f?

• A
• B
• C

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.1

Derivative means the same thing as

• slope of the tangent line

• slope of the normal line

• slope of the secant line

• instantaneous acceleration

7

• A
• B
• C
• D

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

For what values of x does f(x) have a horizontal tangent?

• -3.5, 3.5

• -5, 5

• there are no horizontal tangents

• -5, 0, 5

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11