Question

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.

Answer 1

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