# Math

posted by .

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.

• Math -

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

## Similar Questions

1. ### calculus

For x including [–15, 13] the function f is defined by f(x)=x^7(x+4)^6?
2. ### CALCULUs

For all x in the interval [-11,13] the function f is defined by x^3(x+3)^4 On which two intervals is the function increasing?
3. ### math-calc

for x (-12, 10) the function f is defined: f(x)=x^7(x+2)^2 On which two intervals is the function increasing (enter intervals in ascending order)?
4. ### Calc

f(x) = x^2 / (x - 7)^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. Find the intervals where the function is decreasing. (Enter the interval that contains smaller numbers …
5. ### Calculus

find the intervals where the function is increasing and the intervals where it is decreasing f(x)= (x^3/3)-(x^2/2) ok i found its derivative which is (f1(x)=(x-1)x my options are increasing a) (0,infinity) b) (-1,0) c(-infinity,0)U(1,infinity) …
6. ### calculus

For x ∈ [−12, 10] the function f is defined by f(x) = x7(x + 1)4 On which two intervals is the function increasing (enter intervals in ascending order)?
7. ### Calculous

let f be the function defined by f(x)=12x^2/3 -4X a)find the intervals on which f is increasing I got the rest of the question but I'm still not getting the increasing/decreasing thing
8. ### math

Let f(x) = 3+4x-x^{3}. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). 1. f is increasing on the intervals?
9. ### math

x^2 - 4 What are the: Intervals on which the graph is above the x axis Intervals on which the graph is below the x axis Intervals on which the function is increasing Intervals on which the function is increasing Im not sure how to …
10. ### calculus 1

f(x) = 3x^3 - 9x + 5 find the: 1) zeroes or undefined values 2) intervals where the function is greater than zero 3) intervals where the function is less than zero 4) coordinates of all maxima and minima 5) intervals where the function …

More Similar Questions