The maximum value of f(x) = 2x^3 – 21x^2 + 36x + 7 is

$f' (x) = 6x^2 – 42 x + 36$

$f''(x) = 12x – 42$

Hance $f' (x) = 0\, 6(x^2 – 7x + 6) = 0$

$x = 1 , 6$

$f'' (a) = 12 – 42 = –30 < 0$

f(x) has a maximum at x = 1