Maximum and Minimum Word Problems

On the interval [−2, 2] the function f (x) = x⁴

• (a) has an absolute maximum but no local maxima.
• (b) has an absolute maximum at an interior point of the interval.
• (c) has a local minimum but no absolute minimum.

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• (3.1, 0)

• (0, -1)

• (-3, -55)

• (2, -5)

For each problem, find all points of absolute minima and maxima.

• A

• B

• C

• D

Find the absolute extrema of

g(x) = 3x³ + 6x² on [-1, 1].

• abs max value of 9 when x = 1, abs min value of 3 when x = -1

• abs max value of 9 when x = 1, abs min value of 0 when x = 0

• abs max value of 9 when x = 1, abs min of -1 when x = -1

Given the sign chart for f '(x) and table of f(x), f(x) has ...

• a local maximum at (-10,5).

• an absolute minimum at (-2,0).

• a local minimum at (20,7).

• all of the above