Question

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

Answer 1

Explanation:

f(x) = 4 x - x²

[ f(x+h) - f(x-h) ] / (2h)

= [ 4 (x+h) - (x+h)² - 4(x-h) + (x-h)² ]/ (2h)

= [ 8 h - 4 x h ] / (2 h)

= 4 - 2 x

That is actually the definition of the derivative of the function f(x) with respect to x.