Find and Simplify

Question

Given the function f(x)=3-2x-x² find and simplify (f(x+h)-f(x-h))/(2h)

Answer 1

f(x)=3-2x-x² find and simplify (f(x+h)-f(x-h))/(2h)

f(x+h) = 3 - 2(x+h) - (x+h)^2

f(x-h) = 3 -2(x-h) - (x-h)^2

f(x+h) - f(x-h) = 3 - 2x - 2h - (x^2 + 2xh + h^2) - (3 -2x +2h - (x^2 - 2xh + h^2))

= 3 - 2x -2h -x^2 - 2xh - h^2 -3 +2x -2h + x^2 - 2xh + h^2

= -4h -4xh = -4h(1-x)

(f(x+h)-f(x-h))/(2h) = -4h (1-x) / (2h) = -2(1-x) = 2x - 2