Differentiate each equation with respect to $x$. Leave your answers in terms of only $y$ and $x$.

5. What is $\frac { d ^ { 2 } y } { d x ^ { 2 } }$ for the function in part (a)? Write your answer in terms of $x$ only.

   Hint (e):

   $\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\text{(answer to part (a)) }.$

6. Evaluate $\frac { d ^ { 2 } y } { d x ^ { 2 } } | x = 3$ for the function in part (a).

   Hint (f):

   Translation: Evaluate the 2nd-derivative (that you found in part (e)) at $x = 3$.

7. Write the equation of the tangent line at $x = 3$ for function in part (a).

   Hint (g):

   The equation for the tangent line is $y − y(3) = y^\prime(3)(x − 3)$.

8. If the tangent line is used to approximate the function at $x = 3.01$, will it give an underestimate or an overestimate? Use part (f) to determine your answer.

   Hint (h):

   Is the graph concave up or concave down?