Now it’s time to practice some problems. Do each problem, covering the answer first, then check your
answer.
PROBLEM 1. Sketch the graph of y = x^3 − 9x^2 + 24x − 10. Plot all extrema, points of inflection, and
asymptotes.
Answer: Follow the three steps.
First, see if the x-intercepts are easy to find. This is a cubic equation that isn’t easily factored. So skip
this step.
Next, find the y-intercepts by setting x = 0.
y = (0)^3 − 9(0)^2 + 24(0) − 10 = −10The curve has a y-intercept at (0, −10).
There are no asymptotes, because the curve is a simple polynomial.
Next, find the critical points using the first derivative.
= 3x^2 − 18x + 24Set the derivative equal to zero and solve for x.