Application of derivatives

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

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

Use the sign chart for f'(x).
There is(are) ...

• a local maximum at x = -2.
• a local maximum at x = 4.
• local maxima at x = -2 and x = 4.
• no extrema.

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

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

Tags

CCSS.HSF.IF.B.4

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

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

Tags

CCSS.HSF.IF.B.4

Does this graph have a maximum or minimum value?

• maximum
• minimum
• neither
• both

Tags

CCSS.HSF-IF.C.7A

Does
y = -4x²
have a maximum or minimum value?

• maximum
• minimum
• both
• neither

Tags

CCSS.HSF-IF.C.7A

• max is 4 at x = 0
• max is 4 at x = 3
• max is 3 at x = 5
• No maximum

Tags

CCSS.HSA.REI.D.10

Where is this decreasing?

• (-∞, -2.55) U (0, 2.55)
• (+∞, -6.25) U (36, -6.25)
• (-∞, ∞)
• (-∞, 0)

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If f"(x) >0, what is true about f(x)?

• it is concave up there
• it has an inflection point
• It's zero
• it is concave down there

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression