Find global maxima and global minima of $$f(x)=3(x-2)^{\frac{2}{3}}-(x-2)$$ over the interval $[0,20]$.
My input: Derivative vanishes at $x=10$ and left neighborhood gives positive derivative and right neighborhood gives negative derivative . Therefore $x=10$ is the value where function attains global maxima.(Correct me here if i write something wrong). And i am not able to figure out the global minima. Need help. I saw graph of this function at Desmos but there is a peak at $2$ i am not able to understand that too. At peak we have derivative not defined ?