Question

F(x)=−x3 −x2 +16x+16 1. Calculate f′(x). 2. Calculate f′′(x). 3. Find the x values such that f(x) = 0. Note: this can be done by factoring.

4. Find the stationary point/s. Note: a point requires x and y coordinates.
5. Determine the nature of this/these point/s. 6. Find the point/s of inflection. 7. Determine the limits: limx→∞ f(x) and limx→-∞ f(x). 8. Graph y = f(x) by hand, labelling all important features found in the previous parts. Also, the x and y axes need to be chosen so that all features (including limits) can be seen.
9. Determine the point (x, y) where the function is increasing most rapidly.

Answer 1

just use the [power rule to find the derivative of each term:

d/dx x^n = n*x^(n-1)

As for finding the roots, derivatives don't help much with that. But, digging back into your Algebra I skill set, note that

f(x) = -x^2(x+1) + 16(x+1)
= (16-x^2)(x+1)