Concept explainers
Finding Extrema on a Closed Interval In Exercises 1-8, Find the absolute extrema of the function on the closed interval.
To calculate: The absolute extrema for the function
Answer to Problem 1RE
Solution:
The maximum is
Explanation of Solution
Given:
The function
Formula used:
The point c is considered to be the critical point of the function f if
For the provided function f, the extrema would exist at either the critical point or the end points of the closed interval.
Calculation:
Further differentiating the givenfunction,
To obtain the critical points in the given interval, solve the first derivative to zero.
Calculating the value of the function at these critical points.
We compute the value of the function at the left and right extreme points:-
Therefore, the maximum is
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