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# Obtain a maximum value of the function f(x) x3 - 12x + 11

### Question

Obtain a maximum value of the function f(x) x3 - 12x + 11

### Options

A) -5

B) -2

C) 2

D) 27

The correct answer is D.

### Explanation:

f(x) = x3 - 12x + 11
$$\frac{df(x)}{dx)}$$ = 3x2 - 12 = 0
∴ 3x2 - 12 = 0 $$\to$$ x2m = 4
x = $$\pm$$2, f(+2) = 8 - 24 + 11 = -15
= f(-2) = (-8) + 24 + 11
= 35 - 8 = 27
∴ maximum value = 27

## Dicussion (1)

• f(x) = x3 - 12x + 11
$$\frac{df(x)}{dx)}$$ = 3x2 - 12 = 0
∴ 3x2 - 12 = 0 $$\to$$ x2m = 4
x = $$\pm$$2, f(+2) = 8 - 24 + 11 = -15
= f(-2) = (-8) + 24 + 11
= 35 - 8 = 27
∴ maximum value = 27

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