Find the value of x for which the function f(x) = 2x3 - x2 - 4x + 4 has a maximum value

Find the value of x for which the function f(x) = 2x3 - x2 - 4x + 4 has a maximum value

Answer Details

f(x) = 2x3 - x2 - 4x + 4
f(x) = 6x2 - 2x - 4 at turning point, f1(x) = 0
6x2 - 2x - 4 = 0, 3x2 - x - 2 = 0, 3x2 - 3x + 2x - 2 = 0
(3x + 2)(x - 1) = 0, x = -$\frac{2}{3}$ or 1
f11(x) = 12x - 2,
when x = $\frac{2}{3}$, f11(x) = 12(-$\frac{2}{3}$) - 2 = -10 < 0

$\to$ f(x) is maximum @ x = -$\frac{2}{3}$
when x = 1, f11(x) = 12(1)- 2 = 10 > 0
$\to$ f(x) is maximum @ x = 1