# Finding relative minimum and maximum of a function

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Solve Now ## How do you find the exact relative maximum and minimum of

Example 2: Find the relative maxima and minima of the function f (x) = x 3 - 6x 2 +9x + 15. using the second derivative test. Solution: The given function is f (x) = x 3 - 6x 2 +9x + 15. f' (x) = 3x 2

## The First Derivative Test for Relative Maximum and Minimum

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global

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## How to find relative maximum on the interval by graphing

We look for a function that works. Suppose that \$f'(x)=(x-2)(x-5)\$. Then \$f'(x)\$ is positive for \$x\lt 2\$, negative strictly between \$2\$ and \$5\$, and positive for \$x\gt 5\$. So \$f\$ is

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