# Critical numbers and open intervals

• Nov 23rd 2011, 06:32 PM
eaklemm
Critical numbers and open intervals
I'm stuck on a calculus problem on a practice exam! So if anyone could help me out that would be fantastic!

The equation is y= x^3 + x^2 - 6X

Find all critical numbers and open intervals (increasing and decreasing)

thanks!!
• Nov 23rd 2011, 07:31 PM
pickslides
Re: Critical numbers and open intervals
Solve $\displaystyle \frac{dy}{dx}=0$
• Nov 23rd 2011, 08:00 PM
eaklemm
Re: Critical numbers and open intervals
I guess I dont understand...do you use chain rule? which confuses me as well
• Nov 23rd 2011, 08:06 PM
pickslides
Re: Critical numbers and open intervals
You won't need the chain rule here.

Consider the rule if $\displaystyle y= x^n \implies \frac{dy}{dx}= nx^{n-1}$

If your equation is $\displaystyle y= \frac{x^3}{3}+\frac{x^2}{2}-6x$ use the rule term by term.
• Nov 23rd 2011, 08:34 PM
eaklemm
Re: Critical numbers and open intervals
So would the correct answer be y'= 3x^2 + 2x - 6?
• Nov 23rd 2011, 08:41 PM
pickslides
Re: Critical numbers and open intervals
It would be $\displaystyle y' = x^2 + x - 6$ now solve for $\displaystyle y'=0$