Question

For x∈[−13,10] the function f is defined by:
f(x)=x^7(x+3)^8
How do I find the intervals where the function is increasing?

Answer 1

Calculus:
First derivative test, find zeros, then plug in test numbers between the zeros. Positive is increasing.

Answer 2

I derived and got f'(x)=7x^6(x+3)^8+8x^7(x+3)^7. And found x=-21/15. But that's not within the interval specified.

Answer 3

wait... that's -1.4 and within your bounds

Answer 4

Whoops, I should have added, I'm looking for 2 intervals where the function is increasing. So -1.4, 10 is one.

Answer 5

i'm getting y=0 at x=-3

Answer 6

oh? how?

Answer 7

check that, y=0 at x = -3, 0, -7/5

Answer 8

Graphing calculator. It's not a pretty one. or you can do something like (7x^6+8x^7)(x+3)^8

Answer 9

i think i've found the intervals. How would I find where the function is positive?

Answer 10

Ok, so now that you have those, you plug test numbers into the first derivative equation. if you get back a positive, you have increasing, negative is decreasing

Answer 11

[-13,-3) U (-7/5, 10] seems right, unless you cannot count 0 since it has no slope in the first derivative

Answer 12

Then it would be [-13,-3) U (-7/5, 0) U (0, 10]