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

### Question

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

### Options

A) $$\frac{2}{3}$$

B) 1

C) -1

D) -$$\frac{2}{3}$$

### Explanation:

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

## Dicussion (1)

• 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