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# Local Extrema and Volume of a Solid of Revolution

Please see attached file for full problem description.

The graph of the derivative of a function f is shown below.

(a) Over what intervals is f(x) increasing? decreasing?
Why?
(b) At what x values does f(x) have a local maximum?
Why?
(c) At what x values does f(x) have a local minimum?
Why?
(d) Sketch a possible graph of f(x).

Find the volume of the solid obtained by rotating the region bounded by xy = 4 and about the x-axis.

Let f be a function that is defined and twice differentiable for all values of x and has the following properties:

? f(1) = 3 ? ?
? when
? when
?
Let Find the following

(a) g(1)
(b)

#### Solution Preview

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The graph of the derivative of a function f is shown below.

(a) Over what intervals is f(x) increasing? decreasing?
Observing the figure, we can understand that the derivative of f(x) is positive when x belongs to (-∞, -1)U(0, 2) U(2, ∞), and the derivative is negative for x in (-1, 0)
Why?
The function increases when the ...

#### Solution Summary

Local Extrema and Volume of a Solid of Revolution are investigated.

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