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Graph the equation y= \frac{4x}{x^2 + 1} using first and second derivatives. Indicate the...

Question:

Graph the equation {eq}y= \frac{4x}{x^2 + 1} {/eq} using first and second derivatives. Indicate the coordinates of any local extreme points and inflection points.

Maxima and Minima of functions:

If {eq}\displaystyle f(x) {/eq} is a function then the solutions to the equation {eq}\displaystyle f'(x)=0 {/eq} gives the maximum and minimum values to {eq}\displaystyle f(x) {/eq}.

Inflection points are found at the solutions to the equation {eq}\displaystyle f''(x)=0 {/eq}.

Answer and Explanation:

{eq}\text{for local extremes we have to find critical points}\\ \text{For finding critical points of y, we have to first find out the first...

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