Find f(a + h) - f(a) for the function. Simplify your answer.

Question

f (x)+x^2-11x+1

Answer 1

f(a) = a^2 -11a +1

f(a+h) = (a+h)^2 -11(a+h) +1

f(a+h)-f(a) = a^2 +2ah +h^2 -11a -11h +1 -a^2 +11a -1

= 2ah +h^2 -11h

Answer 2

If f(x) = x² - 11x + 1 then:

f(a + h) = (a + h)² - 11(a + h) + 1 = a² + 2ah + h² - 11a - 11h + 1

f(a) = a² - 11a + 1

So f(a + h) - f(a) = (a² + 2ah + h² - 11a - 11h + 1) - (a² - 11a + 1) = a² + 2ah + h² - 11a - 11h + 1 - a² + 11a - 1 = 2ah + h² - 11h

(you can re-order this if you want to perhaps h² + 2ah - 11h)