f(x)=-8-x^2. What is (f(2+h)-f(2))/h?

Answer 1

For f(x) = -8 - x²:

f(2) = -8 - (2)² = -12

f(2 + h) = -8 - (2 + h)² = -8 - (4 + 4h + h²) = -12 - 4h - h²

f(2 + h) - f(2) = -12 - 4h - h² + 12 = -4h - h² = h(-4 - h)

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