Question

find each of the following for f(x) = 3x² - 6x + 7. (a) f(x + h) (b) f(x + h) - f(x) (c) f(x + h) - f(x) / h (a) f(x + h) = 3x² + 6xh + 3h² - 6x - 6h + 7 (b) f(x + h) - f(x) = 6xh + 3h² - 6h (c) f(x + h) - f(x) / h = \square

Explanation:

Step1: Factor out h from numerator

Given \(\frac{f(x + h)-f(x)}{h}=\frac{6xh + 3h^{2}-6h}{h}\), factor \(h\) from each term in the numerator: \(h(6x + 3h-6)\).

Step2: Cancel out h

Divide the factored numerator by \(h\) (assuming \(h
eq0\)): \(\frac{h(6x + 3h - 6)}{h}=6x+3h - 6\).

Answer:

\(6x + 3h-6\)