2. (20 points) $A$ curve $C$ is defined by the equation
3. (20 points) (a) Show that the equation
has a unique root and that it lies in the interval (−1, 0).
(b) Find the absolute extrema of the function

(b) Find the absolute extrema of the function
4. (20 points) (a) If f : $R$ → $R$ is a differentiable
function and
where $c$ is a constant, what
can be said about $f$?
(b) Assume
compute $f$.

(b) Assume

5. (20 points) Let
(b) Find the intervals of concavity and inflection points of $f$.
(c) Find the horizontal asymptotes of $f$.
(d) Sketch the graph of $f$.
(b) Find the intervals of concavity and inflection points of $f$.
(c) Find the horizontal asymptotes of $f$.
(d) Sketch the graph of $f$.
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