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

smileycellist2

Answered question

2021-06-01

Consider the function f(x)=2x3+6x290x+8,[5,4]
find the absolute minimum value of this function.
find the absolute maximum value of this function.

Answer & Explanation

hosentak

hosentak

Skilled2021-06-02Added 100 answers

Step 1
The function is given by,
f(x)=2x3+6x290x+8
Step 2
Differentiatte with respect to x,
f(x)=6x2+12x90
Solve f(x)=0.
f(x)=0
6x2+12x90=0
x2+2x15=0
(x+5)(x3)=0
x=5,3
Step 3
Find the functional value at x=5.
f(5)=2(5)3+6(5)290(5)+8
=250+150+450+8
=358
Find the functional value at x=3.
f(3)=2(3)3+6(3)290(3)+8
=54+36270+8
=172
The absolute minimum of the given function is -172.
The absolute maximum of the given function is 358.

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