MATHEMATICS

JAMB 2010 - Question 42

Mathematics 2010 JAMB Past Questions - Question 42: At what value of x does the function Y = -3 -2x + x² attain a minimum value?

At what value of x does the function Y = -3 -2x + x² attain a minimum value?
A:
B:
C:
D:
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Correct Answer

A

Explanation

Given that y = -3 - 2x + xsup2,then dy/dx = - 2+2xAt minimum value, dy/dx = 0so - 2 + 2x = 02x = 2therefore x = 2/2=1To find the value of x at which the function Y = -3 - 2x + x² attains a minimum value, we can use calculus. The function Y = -3 - 2x + x² is a quadratic function, and the vertex of a quadratic function represents the minimum or maximum point. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic function.In this case, the quadratic function is Y = x² - 2x - 3, so a = 1 and b = -2.Using the formula x = -b / (2a), we have:x = -(-2) / (2 * 1)x = 2 / 2x = 1Therefore, the function Y = -3 - 2x + x² attains its minimum value at x = 1.