f(x)=x^2-x+1, f(2+h)-f(2) /h

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Please let us go step by step:

Step1: Evaluate f(2) and f(2+h)

f(x)=f(2) means that x=2

so f(2)=2^2-2+1=4-2+1=2+1=3

also

f(2+h) means x=2+h

so f(2+h)=(2+h)^2-(2+h)+1=(2+h)(2+h)-(2+h)+1=4+2h+h^2-2-2h+1=h^2+2h-2h+3=h^2+3

Step2: Now that we know f(2) and f(2+h), let us evaluate f(2+h)-f(2)/h

f(2+h)-f(2)/h=h^2+3-3/h=h^2/h=h

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