Question

Use the graph of f to estimate the local maximum and local minimum. (5 points)

Answer 1

Answer: (A) maximum = (0, 1), minimum = (
`\bold{(3\pi)/(2)}`, -1) and (-π, -1)

Explanation:

The maximum is the highest point on the graph. Which is the vertex of a negative (upside down) parabola.

The minimum is the lowest point on the graph. Which is the vertex of a positive (u-shaped) parabola.

see attachment

Answer 2

The correct option is 1.

Explanation:

In a graph, the lowest points of the functions are called local minima and highest points of the functions are called local maxima.

The point of local maxima and local minima can be more than one point. The graph must be continuous at extreme points.

From the given graph it is noticed that the highest point of the function is (0,1), therefore the local maxima is (0,1).

The lowest points of the graph are

`(-\pi,-1),((3\pi)/(2),-1),(\pi,-1)`

But the graph is discontinuous at
`(\pi,-1)`. So, the point
`(\pi,-1)` is not a local minima.

The point of local minima are
`(-\pi,-1),((3\pi)/(2),-1)`.

Therefore option 1 is correct.