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 !!!
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.
cusps occur where the derivative is undefined, but the function itself is* cusp
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.* relative maximum and minimum
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)* concaved down or up
Hint: use the chain rulei know that first we should find the first and second derivative but i cant diffrentiate it !!!