Finding Relative Maximum and Minimum

**Q1.** Test the Function $\displaystyle g(x)=6x^3-(108)x^2+(630)x-2$ for relative maximum and minimum. Find the critical values. Use the 2nd derivative test if possible.

*My solution:*

$\displaystyle g'(x)=18x^2-216x+630$ if follows that the critical values of g are **x1= -7 **and **x2=-5.**

* To find the critical numbers, I set g'(x) =0. This is where I think I went wrong.

First, I factored out a "6"

$\displaystyle 6(3x^2-36x+105)$

Then, I factored out a 3 and that's how I arrive on my answer of -7 and -5.

**Q.2 (Related to Q1)**

Since $\displaystyle g"(x)=36x-216$ <-- My guess, we have that g"(x1)= ? greater or less than 0 and g"(x2) = ? greater or less than 0. (**I need to find out values for x1 and x2)**

Therefore, by the 2nd derivative test, there is a either a relative max or min when x=x1 and there is a relative max or min when x=x2. **(Choose either or)**

TIA