Consider the function f(x)=1-5x^{2}, -4\le x\le 1. The absolute maximum value

Susan Nall

Susan Nall

Answered question

2021-12-06

Consider the function f(x)=15x2,4x1.
The absolute maximum value is
and this occurs at x equals
The absolute minimum value is
and this occurs at x equals

Answer & Explanation

usumbiix

usumbiix

Beginner2021-12-07Added 33 answers

Step 1
To find the critical points , we solve f'(x)=0
f(x)=15x2
f'(x)=-10x
0=-10x
x=0
Step 2
Then we check the values of f(x) at the endpoints and at the critical points.
At x=-4, f(x)=15(4)2=79 (min)
At x=1, f(x)=15(1)2=4
At x=0, f(x)=15(0)2=1 (max)
Answer: The absolute maximum value is 1
and this occurs at x equals 0
The absolute minimum value is −79
and this occurs at x equals −4

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