Discuss the maxima and minima of the function `f(x)=x^(2/3)-x^(4/3)dot` Draw the graph of `y=f(x)` and find the range of `f(x)dot`

Answer

Points of global maxima: x = opluse(1)/(2sqrt(2))`
Point of local minima :x=0

Explanation

`f(x)-x^(2//3 -x^(4//3)`
`f(x) =(2//3)x^(-1//3)-(4//3)x^(1//3`
critical points : f(x) =0 at x = `(1)/2sqrt(2)`
also f(X) does not exist at x=0
As f(x) is continous at x= 0 it is also a critical point
Sign scheme of f(x) is as follows
Thus x =0 is point of minima and `x = (1)/2sqrt(2)` are point of maxima

also range of f(X) is `(-oo,f) pm(1)/2sqrt(2)`