posted by chelsea .
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)?
If 7 and 4 are exponents, take the derivative.
You should get x^6(x+1)^3(11x+7), setting the derivative equal to zero gives you 0, -1, and -7/11 as critical numbers. Test numbers in the intervals [-12,-1], [-1, -7/11], [-7/11,0] and [0,10]. If the first derivative comes out positive the function is increasing, if negative the function is decreasing. I believe your answers should be [-7/11,0] and [0,10]