**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 $[−1, 1]$.

**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)**

**5.**Calculate the definite integral. Simplify your answer for full credit.

**(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 $dx/dt$.

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