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.