AP CAL AB Topic 5.3-5.9

If the conclusion of the Second Derivative Test is f''(c) = 0, then the test is

If f''(c) > 0, the f is

• Concave down

• Concave Up

• has a relative max

• has a relative min

If (c,(f(c)) is a point of inflection on the graph of f, then f''(c) = o or f'' ___ at x = c.

In topic 5.5, we learned about the Candidates test. This test determines

• Critical points

• Concavity

• Relative Extrema

• Global Max or min

Where f'(x) is increasing

• f(x) is concave down

• f(x) > 0

• f(x) < 0

• f(x)'s line is going down

Relative Extremas occur at ________ ______.

f(c) is the absolute maximum value of f(x) iff f(c) _______ ____ __ _____ for all numbers x in the domain of f(x).

True (T) or False (F) all functions have a maximum or minimum.

Find the Absolute maximum on f(x) = x² +2x + 1 on the interval [-3,0]. Use the Candidates Test.

• f(-3) = 4

• f(-3) = 5

• f(-3) = 6

• f(-3) = 7