critical points (1 Viewer)

[pLuvia]

How do you find the critical points of graphs?
I know from observation
- Discontinuity
- Sharp points i.e. |f(x)|

How do you find it mathematically?

 

[Templar]

A graph is continuous at a if lim x->a+ f(x) = lim x->a- f(x) = f(a), if this condition is not satisfied then there is a discontinuity.

Same for 'sharp points', except replace f(x) with f'(x).

 

[klaw]

when dy/dx is not defined

 

[pLuvia]

A graph is continuous at a if lim x->a+ f(x) = lim x->a- f(x) = f(a), if this condition is not satisfied then there is a discontinuity.

Same for 'sharp points', except replace f(x) with f'(x).

OK thanks .

 

[.ben]

what's it used for?

 

[pLuvia]

Curve sketching, to determine the points on a curve that are undefined

 

[Templar]

In that case wherever the denominator is zero the graph is undefined and approaches +/- infinity.

Any graph resulting from arithmetic operations on polynomials is smooth everywhere except where the denominator is zero.

 

[KeypadSDM]

In that case wherever the denominator is zero the graph is undefined and approaches +/- infinity.

Any graph resulting from arithmetic operations on polynomials is smooth everywhere except where the denominator is zero.

Darn, he said polynomials. WHY COULDN'T YOU SAY POWER SERIES and be wrong for once.