Consider the function f(x)=2x^{3}+9x^{2}-108x+3, -6\le x\le 4. Thus function has an

agreseza

agreseza

Answered question

2021-12-08

Consider the function f(x)=2x3+9x2108x+3,6x4.
Thus function has an absolute minimum value equal to
and an absolute maximum value equal to

Answer & Explanation

jgardner33v4

jgardner33v4

Beginner2021-12-09Added 35 answers

Step 1
f(x)=2x3+9x2108x+3
f(x)=6x2+18x108
f'(x)=0
6x2+18x108=0
x2+3x18=0
(x+6)(x-3)=0
x=-6,3 where 3 and -6 is in the interval [-6,4]
Step 2
So the absolute minima and maxima in the interval will be at any of the x values -6,3 and 4
f(6)=2(6)3+9(6)2108(6)+3=543
f(3)=2(3)3+9(3)3108(3)+3=186
f(4)=2(4)3+9(4)2108(4)+3=451
Therefore,
Absolute minimum value is at 3 and is equal to -186
Absolute maximum value is at -6 and is equal to 543

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?