If f(x)= 4x - x^2, find f(x+h)-f(x-h)/2h

Answer 1

f(x+h) = 4x + 4h - (x² + 2xh + h²) , f(x-h) = 4x - 4h - (x² - 2xh + h²)

f(x+h) - f(x-h) = 8h - 4xh

(f(x+h) - f(x-h)) / 2h = 4 - 2x

Btw, if you slapped a lim as h -> 0 in front, you would have the limit definition of the derivative function