Question

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

Answer 1

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