Mathematics 2005 JAMB Past Questions - Question 39: The maximum value of the functionf(x)=2+x-x2

Correct Answer

A

Explanation

To find the maximum value of the function f(x) = 2 + x - x^2, we can use calculus. First, let's find the derivative of f(x) with respect to x:f'(x) = 1 - 2xNext, we set the derivative equal to zero to find the critical points:1 - 2x = 0Solving for x:2x = 1x = 1/2Now, let's find the second derivative of f(x):f''(x) = -2Since the second derivative is negative, we can conclude that the critical point x = 1/2 corresponds to a maximum value.To find the maximum value, we substitute x = 1/2 into the original function:f(1/2) = 2 + (1/2) - (1/2)^2      = 2 + 1/2 - 1/4      = 2 + 2/4 - 1/4      = 2 + 1/4      = 9/4Therefore, the maximum value of the function f(x) = 2 + x - x^2 is 9/4.