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Explain how to find where a function is increasing most rapidly.

Question:

Explain how to find where a function is increasing most rapidly.

Most Rapid Increase of Function:

The derivative of a function represents the rate at which a function is changing.

The most rapid rate of change of the function is found maximizing the derivative, i.e.

setting the second derivative to zero.

Answer and Explanation:

Let us consider a function of one variable

{eq}y=f(x). {/eq}

The derivative of the function {eq}f'(x) {/eq} represents the rate at which a function is changing at any point x.

The most rapid increase of the function is found maximizing its derivative, that is setting the second derivative to zero

{eq}f''(x) = 0. {/eq}


Learn more about this topic:

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Slopes and Rate of Change

from Math 104: Calculus

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