Find the difference quotient and simplify your answer. f(x) = x2 − 2x + 6, f(5 + h) − f(5) h , h ≠ 0

Question

Find the difference quotient and simplify your answer.

f(x) = x2 − 2x + 6,  f(5 + h) − f(5)

h

, h ≠ 0

Answer 1

f(5) = 21

f(5+h) = (5+h)^2 - 2(5+h) + 6 = (5+h) [(5+h) - 2]+6 = (5+h)(3+h)+6 = h^2 + 8h + 21

or

(25+10h+h^2) - 10 - 2h + 6 = 21 + 8h + h^2

numerator of difference quotient: h^2 + 8h

dividing by h.....

h+8