Mathematics 2009 JAMB Past Questions - Question 38: What value of x will make the function x(4-x) a maximum?

Correct Answer

C

Explanation

x(4-x) = 4x - x² dy/dx = 4 – 2x 4 -2x =0 x = 2To find the value of x that will make the function x(4-x) a maximum, we can use the concept of critical points.First, let's find the derivative of the function with respect to x:f'(x) = 4 - 2xTo find the critical points, we set the derivative equal to zero and solve for x:4 - 2x = 02x = 4x = 2Now, we need to determine whether this critical point is a maximum or minimum. We can do this by examining the second derivative of the function.Taking the derivative of f'(x) = 4 - 2x, we get:f''(x) = -2Since the second derivative is negative, this indicates that the critical point x = 2 is a maximum.Therefore, the value of x that will make the function x(4-x) a maximum is x = 2.