# Local minima

## Main Question or Discussion Point

for the equation... y = x^3 - 2x^2 -5x +2

is its local minima at (2.120,-8.061)

Thanks

How do you find local minima/maxima? First find all the critical points. HOw do you find critical points?
1.f'(x)=0
2.f'(x) does not exist
since your function is a polynomial it means that also it's derivative will be a polynomial of a less degrees, so it will be defined for all real numbers.

Now, after you find the cr. points, how do you distinguish whether it is a local minima or a local maxima?
SInce it is a cubic polynomial there will be max two local extremes.

Say c,d are such cr. points
then c is said to be a local minima if: let e>0, such that e-->0

so f'(c-e)<0,and f'(c+e)>0

and d i said to be a local max, if

f'(d-e)>0 and f'(d+e)<0.

Now do it in particular for your function.

Can you go from here???

i just look at the hessian to figure out if it's a min or not

tiny-tim
Homework Helper
Hi daniel69!

How did you get x = 2.120 ?

i just look at the hessian to figure out if it's a min or not
Look at what?

HallsofIvy