#### MATH 1501

##### Midterm 2 | Summer '15| Barone
1. Consider the function.

(a) Find the intervals where $f(x)$ is increasing and where $f(x)$ is decreasing.

(b) Find and classify any local maximum/minimum of $f(x)$.

(c) Find the absolute maximum/minimum of $f(x)$ on the interval $[−1, 1]$.

2. Find where

3. Use the linearization of the function $f(x) = \sqrt{x}$ at $x = 9$ to estimate $\sqrt{11}$.

4. Find the indefinite integral, do not forget to add an arbitrary constant $C$.
(a)

(b)

(a)

6. A rectangle has its base on the x-axis and its upper two vertices on the parabola $y = 12 - x^2$. What is the largest area the rectangle can have, and what are its dimensions?
7. Assume that and $dy/dt = −2$ when $x = −1$. Find $dx/dt$.