Find Maximum Value of f(x)+x | Derivative Question

[Clu2.0]

1. f(x)=-x²+4x-5 (parabola)

What's the maximum value of "f(x)+x"?


sorry for my english :)

 

[HallsofIvy]

1. f(x)=-x²+4x-5 (parabola)

What's the maximum value of "f(x)+x"?


sorry for my english :)

Since f(x)= -x²+ 4x- 5, f(x)+ x= -x²+ 5x- 5. That can be written as -(x²- 5x- 5. Now complete the square to dotermine where the vertex is.

 

[Clu2.0]

thanks ok find the answer ("1") but in the test answer is 5/4 and teachers says it's correct

 

[stevenb]

Isn't this just a simple case of taking the first derivative with respect to x and setting it equal to zero? This then tells you the value of x where the maximum value occurs. Then substituting this value into the function f(x)+x will tell you the maximum value at that point. This procedure does give the correct answer of 5/4.

 

[Clu2.0]

thanks a lot, my carelessness

 

[hunt_mat]

Or via completing the square.