Find the Maximum/Minimum Value f(x)=-2x^2+9x+1

Problem

ƒ(x)=−2*x2+9*x+1

Solution

1. Identify the type of function. The function ƒ(x)=−2*x2+9*x+1 is a downward-opening parabola because the leading coefficient a=−2 is negative. This means the function has a maximum value at its vertex.

2. Find the x-coordinate of the vertex using the formula x=(−b)/(2*a) Here, a=−2 and b=9

x=(−9)/(2*(−2))

x=9/4

3. Substitute the x-coordinate back into the original function to find the maximum value ƒ(9/4)

ƒ(9/4)=−2*(9/4)2+9*(9/4)+1

4. Simplify the expression to find the final value.

ƒ(9/4)=−2*(81/16)+81/4+1

ƒ(9/4)=−81/8+162/8+8/8

ƒ(9/4)=89/8

Final Answer

Maximum Value=89/8

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