Question

Find the absolute maximum and absolute minimum
values of the function
f (x) = x^4−10x^2−7
on each of the indicated intervals.
Enter None for any absolute extrema that do not exist.
(A) Interval = [−3,−1].
Absolute maximum =-16
Absolute minimum =
(B) Interval = [−4,1].
Absolute maximum =89
Absolute minimum =
(C) Interval = [−3,4].
Absolute maximum =89
Absolute minimum =

I know the absolute value for all would be the same, still trying to find it...any help?

Answer 1

Absolute minimum I meant!

Answer 2

this is three different questions right?

Answer 3

Yeah...but the absolute minimum...i believe is the same for all

Answer 4

\[f (x) = x^4−10x^2−7\]
\[f'(x)=4x^3-20x=4x(x^2-5)=4x(x+\sqrt{5})(x-\sqrt{5})\]

Answer 5

is that right so far?
critical points at \(x=0,x=-\sqrt{5},x=\sqrt{5}\)

Answer 6

so \(-\sqrt{5}, \sqrt{5}\) will give a local min, and 0 will be a local max. now you only have to worry about what interval your are in

Answer 7

So far, I'm not sure...with those answers...I did it that way too but i didn't quite get it...

Answer 8

Hmm is another ex....with all correct answers


Find the absolute maximum and absolute minimum
values of the function
f (x) = x4−4x2−2
on each of the indicated intervals.
Enter None for any absolute extrema that do not exist.
(A) Interval = [−3,−1].
Absolute maximum =43
Absolute minimum =-6
(B) Interval = [−4,1].
Absolute maximum =190
Absolute minimum =-6
(C) Interval = [−3,4].
Absolute maximum =190
Absolute minimum =-6

Is the finding the roots work here as well?