Find the critical (stationary ) points of the function f(X)=`(x^(5))/(20)-(x^(4))/(12)`+5Name these points .Also find the point of inflection

Options

A. no local extreme, one point of inflection
B. Two local maximum one local minimum, two point of inflection
C. one local maximum, one local minimum, one point of inflection
D. one local maximum, one local minimum, two point of inflection

Answer

C

Explanation

`f^(')(x)=(x^(4))/20-(x^(4))/3=(x^(3))/12(3x-4)`
`f^(")(x)=x^(3)-x^(2)=x^(2)(x-1)`
for `xlt0,f^(')(x)gt0` and `xgt0,f^(')(x)gt0`
Hence `x=0` is a point of maxima
also `f^(')(x)=0` where `x=1` but at `x=1` we have an inflection point.
If `x=4/3` is point of minima