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.

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

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

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2. Find where


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

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

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(b)

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5. Calculate the definite integral. Simplify your answer for full credit.
(a)

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(b)

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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?

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7. Assume that and $dy/dt = −2$ when $x = −1$. Find $dx/dt$.

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