Calculus 3.04a - Numerical Derivatives

[@sonamsardar16]

This video really helps elaborate the logic behind the calc techniques I've been mindlessly memorizing in school. Thank you so much!!!! :)

[@florisvandijk6106]

Your way of explaining is so very pleasant and clear and calm

[@kristjandeda5166]

Great explanation

[@nathanobiekwe6836]

This video was really helpful.

[@cagdasalagoz]

we know how to do this with a calc. We need to know how the calc is doing it.

[@ahnafkhan8115]

The derivatives that we find by our differentiation rules are accurate. But we used the forward difference quotient to get those rules. Then shouldn't the forward difference quotient be as accurate as the middle difference quotient?

[@derekowens]

I'll try to help. We can't answer that question without knowing some specifics about the function. The curvature of the function makes the difference quotient just an approximation rather than exact. If the function curves more forward or back of the point in question, that curvature will throw off the value of a forward or backward difference quotient. Unless we are at an inflection point, the error from a forward difference quotient and a backward difference quotient will tend to cancel out, making a symmetrical difference quotient more accurate, as a *general* rule, but not necessarily in every specific case.

[@ahnafkhan8115]

@@derekowens thanks I understand it better now!