Find the difference quotient and simplify your answer.
\[
f(x)=x^{2}-2 x+4, \frac{f(6+h)-f(6)}{h}, h \neq 0
\]

Answer

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Answer

\frac{f(6+h)-f(6)}{h} = \frac{((6+h)^2-2(6+h)+4)-(6^2-2(6)+4)}{h} \Rightarrow \frac{2h+8}{h}

Steps

Step 1 ：f(x)=x^2-2x+4 \Rightarrow f(6)=6^2-2(6)+4

Step 2 ：f(6+h)=(6+h)^2-2(6+h)+4

Step 3 ：\frac{f(6+h)-f(6)}{h} = \frac{((6+h)^2-2(6+h)+4)-(6^2-2(6)+4)}{h} \Rightarrow \frac{2h+8}{h}