Problem

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

Solution

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}

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Source: https://solvelyapp.com/problems/16115/

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