# A critical numbers problem

find the critical number of the function

f(X)= x^3 + 3x^2-24x

f'(X)= 3x^2 + 6x -24

what do i do, next i found the derivative of the function

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arildno
Homework Helper
Gold Member
Dearly Missed
Well, perhaps you should find out either where the derivative equals 23.67, -17 or perhaps some more important value, say 0.

ok so its supposed to equal zero as the definition states for critical numbers,

so i just plug in any numbers in the x's

arildno
Homework Helper
Gold Member
Dearly Missed
so i just plug in any numbers in the x's
Eeh??
Do you know what an equation is, and how to solve it??

i think ido, can u show me an example

yes i know what an equation is, but how do i solve it

hage567
Homework Helper
Can you name what type of equation that is?

well im on the section maximum and minum values, it doesnt say what kind of equation it is, id say its a critical number equation

hage567
Homework Helper
well im on the section maximum and minum values, it doesnt say what kind of equation it is, id say its a critical number equation  Just look at its form. It's a QUADRATIC equation! Have you not learned about those before? There's a formula for finding the roots of a quadratic equation. If you don't know it, look it up.

ok, so when i take the derivative, i just factor it out

hage567
Homework Helper
ok, so when i take the derivative, i just factor it out
What?? I don't understand what you mean by that.

well ive learned about quadratic equations but i forgot what it was called,
well when i factored it out, i got 3(x^2+2x-8) then i factored it out

3(x+2)(x-4) ok thats easy, i forgot about that algebra stuff and trig and geo, like my calculus teacher said, it's not the calculus its all that old stuff that will get ya

i mean 3 (x-2) (x+4)

hage567
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i mean 3 (x-2) (x+4)
OK that's better I was just going to point that mistake out.

yea hey thanks for reminding me about that,

hage567
Homework Helper
No problem. But I would recommend looking up the quadratic formula and remembering it. It works for those times when factoring isn't obvious.