Investigate for the maxima and minima of the function `f(x)=int_1^x[2(t-1)(t-2)^3+3(t-1)^2(t-2)^2]dt`

Options

A. does not have local maxima at `x=1`
B. does not have local minima at `x=7/5`
C. has neither maxima no minima at `x=2`
D. decreasing in `(7/5,oo)`

Answer

C

Explanation

`f(x)=int_(1)^(x)[2(t-1)(t-2)^(3)+3(t-1)^(2)(t-2)^(2)]dt`
`f^(')(x)=(x-1)(x-2)^(2)[2x-4+3x-3]`
`=(x-1)(x-2)^(2)(5x-7)`
maxima at `x=1`, minima at `x=7//5`, neither maxima nor minima at `x=2`