Thread: what is a critical point

For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?

Originally Posted by zintore

For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?

A stationary point of inflection is a critical point.

Originally Posted by zintore

For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?

I have always known "critical points" to be points such that the slope was zero at that point. Inflection points would be critical points of the first derivative.

Originally Posted by Mathstud28

I have always known "critical points" to be points such that the slope was zero at that point.

Yes, critical points are points where the slope is either zero or undefined...but a stationary point is a type of critical point [point where derivative is 0]. So a statitionary point is a critical point, but not all critical points are stationary points...

Just a thought to throw out there.

--Chris