Find the absolute maximum and absolute minimum values of the function
f(x)=x^4−10x^2+3
on each of the indicated intervals.
Enter -1000 for any absolute extrema that does not exist.

(A) Interval = [−3,−1].
Absolute maximum =

Absolute minimum =

(B) Interval = [−4,1].
Absolute maximum =

Absolute minimum =

(C) Interval = [−3,4].
Absolute maximum =

Absolute minimum

Question

Find the absolute maximum and absolute minimum values of the function
f(x)=x^4−10x^2+3
on each of the indicated intervals. 
Enter -1000 for any absolute extrema that does not exist.

(A) Interval = [−3,−1]. 
Absolute maximum =

Absolute minimum =

(B) Interval = [−4,1]. 
Absolute maximum =

Absolute minimum =

(C) Interval = [−3,4]. 
Absolute maximum =

Absolute minimum

campbell_st · Answer

so have you got the 1st derivative and solved to the stationary points...?

anonymous · Answer

what do you mean by that

campbell_st · Answer

ok... well its hard to identify max and min values if you can't differentiate... stationary points are when a tangent has a zero gradient... sometimes called critical values...

anonymous · Answer

yeah i already have my critical points they are sqrt5,-sqrt5 and 0

campbell_st · Answer

ok... so you need to substitute

x = -1, x = -sqrt(5) and x = -3 into the original equation to see which has the largest y value

that is how you find the answer to part (a)

campbell_st · Answer

an easy way to do this problem is to use some graphing software... 

means no calculus...

anonymous · Answer

im still a bit confuse do i plug in these values into the derivtive and also where did these values come from

campbell_st · Answer

no plug then into the original equation... 

y = (-3)^4 - 10(-3)^2 + 3 
  = 81 - 90 + 3

y = -6

x = - sqrt(5) 

y = (-sqrt(5)^4 - 10(-sqrt(5)^2 + 3

y = 25 - 50 + 3

y = -22

x = -1

so the absolute maximum are x = -3 and x = -1 when y = -6

y = (-1)^4 - 10(-1)^2 + 3

y = 1 - 10 + 3

y = -6

campbell_st · Answer

and absolute min is y = -23 when x = -sqrt{5}

anonymous · Answer

does it matter in what interval i put it

anonymous · Answer

i put that as the answer for part a as the minimum but it says its wrong

campbell_st · Answer

where here is a graph of your function

anonymous · Answer

thank you hopefully i get t right lol

campbell_st · Answer

well its interesting it doesn't see y = -22 as the min on the interval [-3, -1]

campbell_st · Answer

hope it helps...

anonymous · Answer

dude ask her for a nudes unless shes like 10 years old shes a dumb bimbo

anonymous · Answer

ill try to ignore that comment but thanks again :) campell

anonymous · Answer

bye bimbo face