How do you find all local maximum and minimum points given $y=x^3-9x^2+24x$ ?

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Answer 1 · 2016-11-07T23:12:59

Let $f(x)=x^3-9x^2+24x$

Find where $f(x)$ has a slope of zero. This is the same as finding points where $f'(x)$ is equal to zero.

Find $f'(x)$ using the power rule:
$f'(x)=3x^2-18x+24$

Find where $f'(x)$ is equal to zero by factoring:
$0=3[x^2-6x+8]$
$0=3(x-4)(x-2)$

$x=4, x=2$

Plug in values in between these numbers to test whether each is a local max or min

$x=2$ is a local maxima, and $x=4$ is a local minima

How do you find all local maximum and minimum points given y=x^3-9x^2+24xy=x^3-9x^2+24x?