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First and second derivative tests


Use the commands that you learned in the first four labs to complete these exercises.


For each exercise below, do NOT look at a plot of the function. You may however, plot the derivative to help you if you need it.
  1. For the function $\displaystyle f(x) = \frac{x^2-x+9}{x^2-x-12}$,
    1. Find all critical values (where the derivative is zero or undefined).
    2. Find intervals on which $f$ is increasing and the intervals on which it is decreasing.
  2. For the function $\displaystyle g(x)=\frac{1}{\sqrt{x^3+3x^2-9x+24}}$
    1. Find all critical points. (You do not need to consider where the derivative is undefined here because there could never be a relative extrema at a point where $g'$ is undefined. Also remember a critical point implies finding corresponding $y$ values for each critical value.)
    2. Use the second derivative test to classify each point as a relative maximum or a relative minimum, again, without plotting the function.

Jane E Bouchard