Explanation

(c)
Given, $f(x) = 2x^{3} - 21x^{2} + 36x - 30$
$\Rightarrow \ \ \ \ f^{'}(x) = 6x^{2} - 42x + 36$
For maxima or minima, put $f^{'}(x) = 0$
$\Rightarrow \ 6x^{2} - 42x + 36 = 0\ \ \ \Rightarrow \ \ \ \ x = 6,\ 1$
And $f^{''}(x) = 12x - 42$
$f^{''}(1) = - 30$ and $f^{''}(6) = 30$
Hence, $f(x)$ has maxima at $x = 1$ and minima at $x = 6$