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The maximum value of the function of y = 2 + 3x - 4x\(^2\) is


Question

The maximum value of the function of y = 2 + 3x - 4x\(^2\) is

Options

A) -23/16

B) 5/15

C) 41/16

D) 59/16

The correct answer is C.

Explanation:

\(y = -4x^2 + 3x + 2\)
\(a = -4, b = 3, c = 2\)
max \(= c - \left( \cfrac{b^2}{4a} \right)\)
\(= 2 - \left( \cfrac{3^2}{4(-4)} \right)\)
\(= 2 + \cfrac{9}{16}\)
\(= \cfrac{32 + 9}{16} = \frac{41}{16}\)

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