college Algebra

Question

Give the function g (x) = 5-x^2, simplify g(x + h) -g(x), h=0

h

Answer 1

g(x+h) = 5 - (x+h)^2 = 5 - x^2 - 2xh - h^2

g(x+h) - g(x) = -2xh - h^2

dividing by h: -2x - h

as h tends to zero the difference quotient becomes -2x