Which of the following hold(s) good for the function `f(x)=2x-3x^(2/3)?` `f(x)` has two points of extremum. `f(x)` is convave upward `AAx in Rdot` `f(x)` is non-differentiable function. `f(x)` is continuous function.

Options

A. f(x) has two points of extremum
B. f(x) is convace upward `forall x in R`
C. f(x) is non differentiable function
D. f(x) is continuous function

Answer

1,2,3,4

Explanation

`f(x)=2-2x^(-1//3)= 2(1-(1))/(x^(1//3))=2(x^(1//3)-1)/(x^(1//3))`
Sign schem of derivation is as follows

f(X) has point of maxima at x=0 and point of minima at x=1 also f(x) is non differentiable at x=0