Question

find the critical numbers
10x^3+10x^2-10x

Answer 1

i thought the numbers were 1/3 and -1
but this is wrong
please help im not sure what im doing wrong

Answer 2

Your critical numbers meaning the zeroes to this polynomial?
if then, it can be factored to
\(10x(x^2 + x +1)\), i.e one of them is zero.
where the quadratic can be factored by the general factor formula. Do you need further assistance?

Answer 3

\[f'(x)=10x*d/dx(x^2+x-1)\]
\[10x(2x+1)\]
so i got for my critical values to be 0 and -1/2
this is still wrong

Answer 4

Fisrt you have to take the derivitive of the original function. The reason is because your trying to find when the slope of the original funcition is zero. So the first derivitive of 10x^3+10x^2-10x is 30x^2 + 20x-10. now find the zeros of this function to find the critical numbers.

Answer 5

Aye. Your derivative did not account for the chain rule.

Answer 6

if i take it from the beginning it gives me 5/15 and -1

Answer 7

how do i use the chain rule in this problem

Answer 8

It's best you don't, but anyway,
\[\frac{ d }{ dx }(10x(x^2 + x+1))= 10x(2x+1)+10(x^2 + x+1)\] simplify and find the zeroes.

Answer 9

if it is best not to, then how should i solve this problem?

Answer 10

Just differentiate it like Rob did. However, this time, don't factor the 10x out.
\[\frac{ d }{ dx }(10x^3+10x^2-10x)=30x^2+20x-10\]
Wait a minute. Your answers are right. Are you sure you are wrong?

Answer 11

I put in my answer wrong so i kept coming out, this time its right so never-mind but thanks for your time

Answer 12

Lol okay. You're welcome :)