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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) \(\frac{1}{2}\)

The correct answer is B.

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 = -\(\frac{1}{2}\)

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