Consider the function f(x)=4-5x^{2}, \ \ \ -3\le x\le 2. The

namenerk

namenerk

Answered question

2021-12-09

Consider the function f(x)=45x2,   3x2.
The absolute maximum value is B
and this occurs at x= B
The absolute minimum value is B
and this occurs at x= B

Answer & Explanation

Jacob Homer

Jacob Homer

Beginner2021-12-10Added 41 answers

Step 1
Given f(x)=45x2,   3x2
we find absolute maximum and minimum value.
Step 2
Since f(x)=45x2
then f'(x)=-10x
for critical point f'(x)=0
10x=0
x=0 critical point
and
f(x)=45x2
then f(-3)=-41
f(-2)=-16
f(-1)=-1
f(0)=4
f(1)=-1
f(2)=-16
Hence the absolute maximum value =4
and this occurs at x=0
The absolute minimum value =-41
and this occurs at x=-3

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