Find the value of x for which the function f x ... - JAMB Mathematics 2007 Question

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