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

f(x) has maximum at x = 1

We have,

$f(x) =2 x^3-21 x^2+36 x-30$

$\Rightarrow f'(x) =6 x^2-42 x+36$ and $f''(x)=12 x-42$

At points of local maximum or minimum, we must have

$f'(x)=0 \Rightarrow 6\left(x^2-7 x+6\right)=0 \Rightarrow x=1,6$

Clearly, f''(1) = 12 - 42 = -30 < 0 and f(6) = 72 - 42 > 0

So, f(x) has local maximum at x = 1 and local minimum at x = 6.