Question

Find and simplify the following for f(x) = x(19-x), assuming h+0 in (C).
(A) f(x + h)
(B) f(x + h) – f(x)
f(x +h)-f(x)
(C)
h
(A) f(x + h) =
(Simplify your answer.)
B and c solve

Answer 1

Answer:  see below

Step-by-step explanation:

f(x) = x(19 - x)

     = 19x - x²

A) f(x+h) = (x + h)[19 - (x + h)]

             = (x + h)(19 - x - h)

             = 19x - x² - 2xh + 19h - h²

B) f(x+h) - f(x) = (19x - x² - 2xh + 19h - h²) - (19x - x²)

                     = - 2xh + 19h - h²

                     = h(-2x + 19 - h)

C) [f(x+h) - f(x)]/h = [h(-2x + 19 - h)]/h

                           = -2x + 19 - h

As h → 0:           = -2x + 19