Given f(x)= x^2 -3x......?

Question

Simplify:

f(x+ h)

(f(x+h) - f(x))/ h

Answer 1

f(x) = x² - 3x

f(x + h) = (x + h)² - 3(x + h)

f(x + h) = (x + h)(x + h) - 3x - 3h

f(x + h) = (x² + xh + xh + h²) - 3x - 3h

f(x + h) = x² + 2xh - 3x + h² - 3h

f(x + h) = (x + h)(x + h - 3)

(f(x + h) - f(x)) / h = ((x + h)(x + h - 3) - x² + 3x) / h

(f(x + h) - f(x)) / h = (x² + 2xh - 3x + h² - 3h - x² + 3x) / h

(f(x + h) - f(x)) / h = (2xh + h² - 3h) / h

(f(x + h) - f(x)) / h = 2x + h - 3

Hope this helps you!