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3 years ago

The diameter and height of this cylinder are equal to the side length,S,of the cube in which the cylinder is imscribed. What is

the expression for the cylinder's volume?

Mathematics

1 answer:

max2010maxim [7]3 years ago

3 0

$V=B\times H$
$V=\pi r^{2}h$
$V=\pi (\frac{d}{2})^{2}h$
$V=\pi (\frac{s}{2})^{2}s$
$V=\pi (\frac{s^{2}}{4})s$
$V=\frac{\pi s^{3}}{4}$

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<u>Increasing and Decreasing Intervals of Functions</u>

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

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We find the critical points equating f'(x) to zero

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Simplifying by -6

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We get the critical points

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They define the following intervals

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