Question

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?

Find the region in which the function is positive

Answer 1

Evaluate the derivative of f. The function is increasing where the derivative >0. It increases for x between -11 and -3 and between 0 and +13

The points where f(x) = 0 are x=0 and x=-3. At x>0, it is positive.