Given f(x)=8x-2x^2-5, find the maximum value of the function f(x).

Note that this is a quadratic function whose graph opens down.  You could plot this function and note the coordinates of the vertex; the y-coordinate would be the max value of the function.

Alternatively, find x = -b/(2a), where a = -2, b = 8 and c = -5.  Then find the corresponding y-value.

Alternatively, find the derivative of f(x) and set it = to 0.  Solve for x.  Find the y value associated with this x.  That y-value is the max of f(x).