Chapter 6, Problem 19MCQ

To determine

Find the x -coordinates at which the relative maxima and minima occur using graph.

Answer to Problem 19MCQ

The x-coordinates of the relative maxima is $x=1$ and the minimums are $x=-1$ and $x=4$ .

Explanation of Solution

Given:

The given graph is

  

Calculation:

In the graph, the point is a relative maximum of the function since no other nearby points have a greater y -coordinate. The graph is increasing as it approaches the point and decreasing at it moves from the point.

Relative maximum is $x=1$ .

In the graph, the point is a relative minimum of the function since no other nearby points have a lesser y -coordinate. The graph is decreasing as it approaches the point and increasing at it moves from the point.

Relative minimums are $x=-1$ and $x=4$ .

Hence the x -coordinates of the relative maxima is $x=1$ and minimums are $x=-1$ and $x=4$ .