# Thread: Critical numbers and open intervals

1. ## 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!!

2. ## Re: Critical numbers and open intervals

Solve $\displaystyle \frac{dy}{dx}=0$

3. ## Re: Critical numbers and open intervals

I guess I dont understand...do you use chain rule? which confuses me as well

4. ## 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.

5. ## Re: Critical numbers and open intervals

So would the correct answer be y'= 3x^2 + 2x - 6?

6. ## Re: Critical numbers and open intervals

It would be $\displaystyle y' = x^2 + x - 6$ now solve for $\displaystyle y'=0$