Given the function g(x) = 6 − x2, evaluate g(x + h) − g(x) h , h ≠ 0.

Answer 1

g(x) = 6 - x²

[g(x+h) - g(x)] / h = [6 - (x+h)² - (6 - x²] / h

= [6 - x² - 2xh - h² - 6 + x²] / h = [-2xh - h²] / h = h(-2x - h) / h = -2x - h