View source for How to finding Local Maxima and Minima by Differentiation

Our example will be :
<math> f(x)= x^3-12x+1 </math>
And the graph will be the one at the side.
[[File:Screen Shot 2021-07-31 at 9.35.59 PM.png|thumb]]
Then we will need to use the derivatives to find the two-point that has 0 slopes we will also call it Local maxima and Local minima

<math> f'(x)=3x^2-12 </math>
 
<math> f'(x)=3x^2-12</math>

<math> 3x^2=12</math>

<math> x^2=4 </math>

Then we get x=2 and x=-2 so then we put them into the function.

<math>f(x)= 2^3-(12*2)+1=-15</math>

<math>f(x)= -2^3-(12*-2)+1= 17</math>

so the first point will be local maxima it will be at (-2,17)  and then local minima (2,-15).

[[File:Screen Shot 2021-07-31 at 9.55.12 PM.png|thumb]]