Math
posted by Jay111 .
For x [–14,13] the function f is defined by
f(x)=(x^3)(x+6)^4
On which two intervals is the function increasing (enter intervals in ascending order)?
I got increasing intervals between [14, 6], but can't find the other increasing interval. I believe it is [3, 13] but I get the answer is wrong. Thanks again.

The places where the function changes from increasing to decreasing are where f'(x) = 0
f'(x) = 3x^2(x+6)^4 + 4(x+6)^3*x^3
= (x+6)^3 [7x^3 +18x^2]
I can see that becoming zero at x=0, x=6, and x = 18/7, but not at x=3
recheck your numbers and mine