Mathematics 2008 JAMB Past Questions - Question 38: Find the minimum value of the function y=x(1+x).

Correct Answer

B

Explanation

y = x (1+x)y = x +xsup2dy/dx = 1+2xat minimum dy/dx = 0therefore 1+2x = 0 2x = -1To find the minimum value of the function y = x(1 + x), we can use calculus. First, let's find the derivative of the function with respect to x:dy/dx = 1 + 2xTo find the minimum value, we set the derivative equal to zero and solve for x:1 + 2x = 02x = -1x = -1/2Now, let's find the second derivative to determine if this critical point is a minimum or maximum:d²y/dx² = 2Since the second derivative is positive (2 > 0), the critical point x = -1/2 corresponds to a minimum value.To find the minimum value of y, substitute x = -1/2 back into the original function:y = (-1/2)(1 - 1/2)y = (-1/2)(1/2)y = -1/4Therefore, the minimum value of the function y = x(1 + x) is -1/4.x = -1/2