2.

**(20 points)**$A$ curve $C$ is defined by the equation Find the equation of the tangent line to $C$ at the point of intersection of $C$ with the positive x-axis.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 on the interval [−1, 2].

(b) Find the absolute extrema of the function on the interval [−1, 2].

4. (20 points) (a) If f : $R$ → $R$ is a differentiable
function andwhere $c$ is a constant, what
can be said about $f$?

(b) Assume compute $f$.

(b) Assume compute $f$.

5.

(b) Find the intervals of concavity and inflection points of $f$.

(c) Find the horizontal asymptotes of $f$.

(d) Sketch the graph of $f$.

**(20 points)**Let (a) Find the intervals of monotonicity and extrema 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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