If `f(x)=3x^(3)-9x^(2)-27x+15`,t hen the maximum value of `f(x)` is

Options

A. `-66`
B. `30`
C. `-30`
D. `66`

Answer

B

Explanation

We have,
`f(x)=3x^(2)-9x^(2)-27x+15`
`impliesf(x)=9x^(2)-18x-27`
For maxima or minima, we put `f(x)=0`
`implies9x^(2)-18-27=0`
`impliesx^(2)-2x-3=0`
`implies(x-3)(x+1)=0 impliesx=-1,3`
Now, `f'''(x)=18x-18`
at `x=-1,f''(x)=18(-1)-18=-36 lt 0`
So, x=-1, point of maxima
`therefore`Maximum value of f(x) at x=-1 is
`f(-1)=3(-1)^(3)-9(-1)^(2)-27(-1)+15`
`=-3-9+27+15=12+42=30`