Consider the function f(x)=2x^{3}+6x^{2}-90x+8, [-5,4] find the absolute minimum value of this function. find the absolute maximum value of this function.

smileycellist2 2021-06-01 Answered
Consider the function \(f(x)=2x^{3}+6x^{2}-90x+8, [-5,4]\)
find the absolute minimum value of this function.
find the absolute maximum value of this function.

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Expert Answer

hosentak
Answered 2021-06-02 Author has 28112 answers

Step 1
The function is given by,
\(f(x)=2x^{3}+6x^{2}-90x+8\)
Step 2
Differentiatte with respect to x,
\(f'(x)=6x^{2}+12x-90\)
Solve \(f'(x)=0\).
\(f'(x)=0\)
\(6x^{2}+12x-90=0\)
\(x^{2}+2x-15=0\)
\((x+5)(x-3)=0\)
\(x=-5,3\)
Step 3
Find the functional value at \(x=–5.\)
\(f(-5)=2(-5)^{3}+6(-5)^{2}-90(-5)+8\)
\(=-250+150+450+8\)
\(=358\)
Find the functional value at \(x=3\).
\(f(3)=2(3)^{3}+6(3)^{2}-90(3)+8\)
\(=54+36-270+8\)
\(=-172\)
The absolute minimum of the given function is -172.
The absolute maximum of the given function is 358.

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