least value of the function `f(x)=2x^3-3x^2-12x+1` on `[-2,2.5]`

Options

A. `-3`
B. `8`
C. `-19`
D. `16.5`

Answer

A

Explanation

Let f(X)`=2x^(3)-3x^(2)-12x+1`
`rarrf(x) =6x^(2)-6x-123` ltrbgt put f(X) =0 for maxima or minima
`rarr 6x^(2)-6x-12=0 rarr x^(2)-x02 =0`
`rarr (x-2)(x+1)=0`
Now `f''(x)=12x-6`
`rarr f''(2) =24-6=18 gt 0` ltrbgt since f''(x) is ve at x=2
`therefore` f(X) is minimum at x=2
=16-12-24+1=-19