Question

for each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum. (enter your answers as a comma - separated list.) absolute maximum absolute minimum local maximum local minimum neither a maximum nor a minimum

Explanation:

Step1: Recall definitions

An absolute maximum is the highest point on the entire graph, an absolute minimum is the lowest point on the entire graph. A local maximum is higher than its immediate - neighbors, and a local minimum is lower than its immediate - neighbors.

Step2: Analyze point a

At point a, it is a local maximum as the function value at a is higher than the values of the function in the immediate neighborhood.

Step3: Analyze point b

At point b, it is a local minimum as the function value at b is lower than the values of the function in the immediate neighborhood.

Step4: Analyze point c

At point c, it is a local maximum as the function value at c is higher than the values of the function in the immediate neighborhood.

Step5: Analyze point d

At point d, it is a local minimum as the function value at d is lower than the values of the function in the immediate neighborhood.

Step6: Analyze point r

At point r, it is a local minimum as the function value at r is lower than the values of the function in the immediate neighborhood.

Step7: Analyze point s

There is no information about the behavior of the function beyond s. But from the visible part of the graph, it is neither a maximum nor a minimum.

Answer:

absolute maximum: none
absolute minimum: none
local maximum: a, c
local minimum: b, d, r
neither a maximum nor a minimum: s