If `f(x)=2x^(3)-21x^(2)+36x-30`, then which one of the following is correct?

Options

A. f(x) has minimum at x=1
B. f(x) has maximum at x=6
C. f(x) has maximum at x=1
D. f(x) has no maximum of minimum

Answer

C

Explanation

we have
`f(x)=2x^3-21x^2+36x-30`
`rArr f(x) = 6x^2-42 x+ 36 ` and `f(x)=12x-42`
At points of local maximum or minimum , we must have
`= f(1)= 12 -42 =-30 lt 0 and f(6)= 72 -42 gt 0 `
So f(x) hasiocal maximum at x= 1 and local minimum at x=6