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.
1 answer
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