find the absolute minimum value of the function f(x) = 1/4x^4 + x^3 - 5x^2

Question

shamil98 · Answer

Are you allowed to use calculus? or is this for algebra 2?

anonymous · Answer

This is calculus

shamil98 · Answer

You start by taking the first derivative right?

anonymous · Answer

Yes, I took the first derivative but after that I'm not sure. I can set it to zero but I'll have an x in all my numbers. I could factor out the x but after doing that and then setting it to zero, I don't get the right answer

shamil98 · Answer

f(x) = 1/4x^4 + x^3 - 5x^2
f'(x) = x^3 + 3x^2 - 10x
0 = x^3 + 3x^2 - 10x
0 = x(x^2 + 3x - 10)
0 = (x+5)(x-2)
can you do it from here?..

shamil98 · Answer

btw 1/4x^4  derived is
4/4x^3
which is just x^3, if you're wondering

anonymous · Answer

That is what I did initially however the answer in my book shows -93.75

shamil98 · Answer

your book isn't wrong.

shamil98 · Answer

(x+5)(x-2) = 0
x = -5 , x = 2

evaluate x at -5
f(x) = 1/4x^4 + x^3 - 5x^2
you get -93.75

anonymous · Answer

ahhhhhhhhhh, yes i see it now. Thank you very much!

shamil98 · Answer

Glad to be of help.