Increasing/ Decreasing intervals

For x ∈ [−12, 11] the function f is defined by

f(x) = x3(x + 6)^6

On which two intervals is the function increasing (enter intervals in ascending order)?

Find the region in which the function is positive: to

Where does the function achieve its minimum?

when i derived it i got

3x^2(x+6)^6 + 6x^3(x+6)^5

then you set it equal to zero... how do i use the algebra part now?

I tried something like this:

(x+6)^5 [3x^2(x+6)+ 6x^3]

please help!

I got all the answers now but the last....

when does it reach it's minimum?

Re: URGENT! DUE 12 AM!! Increasing/ Decreasing intervals

Quote:

Originally Posted by

**habibixox** For x ∈ [−12, 11] the function f is defined by

f(x) = x3(x + 6)^6

On which two intervals is the function increasing (enter intervals in ascending order)?

Find the region in which the function is positive: to

Where does the function achieve its minimum?

when i derived it i got

3x^2(x+6)^6 + 6x^3(x+6)^5

then you set it equal to zero... how do i use the algebra part now?

I tried something like this:

(x+6)^5 [3x^2(x+6)+ 6x^3]

please help!

I got all the answers now but the last....

when does it reach it's minimum?

You are correct so far. Since you now have two factors that multiply to give 0, at least one of them must be 0.

So (x + 6)^5 = 0 or 3x^2(x + 6) + 6x^3 = 0

You can factorise the second equation further...