Find the points of inflection for (i)`f(x)=sinx` (ii) `f(x)=3x^4-4x^3` (iii) `f(x)=x^(1/3)`

Explanation

f(x)=cosx
`rArr` f(x)(=cosx)
`rArr` f(x)=-sinx
f(x)=0
`rArr x=npi,nin Z`
So points of inflection are x= `npi,ninz`
All all points of inflection tangent crosses the curved

(ii) `f(x)=3x^(4)-4x^(3)`
`therefore f(x)=12x^(3)-12x^(2)`
`rArr f(x)=36x^(2)-24x`
Now f(x)=0
`rArr x=0,2//3`which are points of inflection

We observe that tangents to the curve at x =0 and x =`(2)/(3)` are crossing the curve.