Question

find each of the following for $f(x) = 3x^2 - 6x + 7$.\
(a) $f(x + h)$\
(b) $f(x + h) - f(x)$\
(c) $\dfrac{f(x + h) - f(x)}{h}$\
\
(a) $f(x + h) = 3x^2 + 6xh + 3h^2 - 6x - 6h + 7$\
(b) $f(x + h) - f(x) = \square$

Explanation:

Step1: Recall \( f(x+h) \) and \( f(x) \)

We know \( f(x + h)=3x^{2}+6xh + 3h^{2}-6x - 6h + 7 \) and \( f(x)=3x^{2}-6x + 7 \).

Step2: Subtract \( f(x) \) from \( f(x+h) \)

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Answer:

\( 6xh + 3h^{2}-6h \)