HW 21 Written Part (due Wed 3/22)
Please complete the following problems.
#1 Suppose that $f$ is a function that is continuous except at $x = 2$, where it has a vertical
asymptote. Suppose also that the first derivative of $f$ is given by
$$f'(x) = \frac{e^x(x+4)(x-1)^2}{x-2}$$
To reiterate, the above formula is the derivative of $f$, not $f$ itself! You don't need to take any
derivatives for this problem because it is already done!
(a) Determine all the critical numbers of $f$.
(b) Determine the intervals where $f$ is increasing and decreasing.
(c) Decide whether $f$ has a local max, local min, or neither at each critical number.
(d) Sketch a possible graph of $y = f(x)$. (Note that you do not need, and it is not
recommended, to try to find a formula for $f(x)$!)
