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# Find the minimum value of the function y = x(1 + x)

### Question

Find the minimum value of the function y = x(1 + x)

### Options

A) -$$\frac{1}{4}$$

B) -$$\frac{1}{2}$$

C) $$\frac{1}{4}$$

D) $$\frac{1}{2}$$

### Explanation:

y = x(1 + x)
y = x + x2
$$\frac{dy}{dx}$$ = 1 + 2x
at minimum $$\frac{dy}{dx}$$ = 0
therefore, 1 + 2x = 0 $$\to$$ 2x = -1
x = -$$\frac{1}{2}$$

## Dicussion (1)

• y = x(1 + x)
y = x + x2
$$\frac{dy}{dx}$$ = 1 + 2x
at minimum $$\frac{dy}{dx}$$ = 0
therefore, 1 + 2x = 0 $$\to$$ 2x = -1
x = -$$\frac{1}{2}$$