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JAMB Mathematics 2010 Paper

Question : 27

Total: 49

At what value of X does the function y = -3 - 2x + X2 attain a minimum value?

Solution:

Concept:

A function attains a minimum when its derivative is zero and the second derivative is positive.

Explanation:

Given

y = -3 - 2x + x^2

Differentiate with respect to

x

\frac{dy}{dx} = -2 + 2x

Set

\frac{dy}{dx} = 0

for a turning point:

-2 + 2x = 0

2x = 2

x = 1

Confirm it is a minimum:

\frac{d^2y}{dx^2} = 2 > 0

Thus, the function has a minimum value at

x = 1

Answer:

x = 1

(Option D).

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