Thread: differentiation

the curve f(x) = x-3(x-1)^1/3
how to find if it :
* has stationary points
* cusp
* relative maximum and minimum
* concaved down or up

i know that first we should find the first and second derivative but i cant diffrentiate it !!!

Originally Posted by wutever

the curve f(x) = x-3(x-1)^1/3
how to find if it :
* has stationary points

stationary points occur where the derivative is zero. (you may have to do further tests. for instance, if the second derivative is zero at the same point, it MAY be an inflection point.

* cusp

cusps occur where the derivative is undefined, but the function itself is

* relative maximum and minimum

relative maximums occur at points where the first derivative is zero and the second derivative is negative. minimums occur where the first derivative is zero and the second derivative is positive.

* concaved down or up

a function is concave down where the second derivative is negative. it is concave up where the second derivative is positive. (don't look for points here, look for intervals)

i know that first we should find the first and second derivative but i cant diffrentiate it !!!

Hint: use the chain rule