Question

find the absolute maximum and minimum values of the following function on the given interval. then graph the function. g(x)=\sqrt{1 - x^{2}}, 0\leq x\leq1. find the absolute maximum value. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. the absolute maximum value 1 occurs at x = 0. (type exact answers, using radicals as needed. use a comma to separate answers as needed.) b. there is no absolute maximum. find the absolute minimum value. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. the absolute minimum value occurs at x =. (type exact answers, using radicals as needed. use a comma to separate answers as needed.) b. there is no absolute minimum.

Explanation:

Step1: Evaluate function at endpoints

For \(x = 0\), \(g(0)=\sqrt{1 - 0^{2}}=1\). For \(x = 1\), \(g(1)=\sqrt{1-1^{2}} = 0\).

Step2: Analyze function behavior

The function \(y=\sqrt{1 - x^{2}}\) on \(0\leq x\leq1\) is non - negative and decreasing on the given interval.

Answer:

A. The absolute minimum value \(0\) occurs at \(x = 1\)