Question

For the function: f(x) = 3x^2– 4x – 8, find and simplify

A. f(x) - f(a) divided by x-a

b.f(x +h) - f(x) all divided by H

Answer 1

Answer:

Step-by-step explanation:

A)  (f(x) - f(a)) / (x - a)

(3x²– 4x – 8 - (3a² – 4a – 8)) / (x - a)

(3x²– 4x – 8 - 3a² + 4a + 8) / (x - a)

(3(x² - a²) – 4(x - a)) / (x - a)

(3(x - a)(x + a) – 4(x - a)) / (x - a)

3(x + a) - 4

B)  (f(x + h) - f(x)) / h

(3(x + h)² -  4(x + h) - 8 - (3x² - 4x - 8)) / h

(3(x² + 2xh + h²) -  4x - 4h - 8 - 3x² + 4x + 8) / h

(3x² + 6xh + 3h² -  4x - 4h - 8 - 3x² + 4x + 8) / h

(3x² + 6xh + 3h²         - 4h - 8 - 3x²         + 8) / h

(3x² + 6xh + 3h²         - 4h       - 3x²              ) / h

(          6xh + 3h²         - 4h                            ) / h

(6xh + 3h² - 4h) / h

6x + 3h - 4