The maximum value of the function
f(x) = 2 + x - x\(^2\) is
A
\(\frac{9}{4}\)
B
\(\frac{7}{4}\)
C
\(\frac{3}{2}\)
D
\(\frac{1}{2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
f(x) = 2 + x - x2
dy/dx = 1-2x
As dy/dx = 0
1-2x = 0
2x = 1
x = 1/2
At x = 1/2
f(x) = 2 + x - x2
= 2 + 1/2 -(1/2)2
= 2 + 1/2 - 1/4
= (8+2-1) / 4 = 9/4
Source: Myschool Past Questions Archive (Record #8497)