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The maximum value of the function
f(x) = 2 + x - x

The maximum value of the function
f(x) = 2 + x - x2 is

A.

9/4

B.

7/4

C.

3/2

D.

1/2

View answer & explanation

Correct answer is A

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

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