In Exercises $87-92,$ find the difference quotient and simplify your answer. $$ f(x)=x^{2}-x+1, \quad \frac{f(2+h)-f(2)}{h}, \quad h \neq 0 $$
Added by Heather M.
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$f(2+h) = (2+h)^2 - (2+h) + 1 = 4 + 4h + h^2 - 2 - h + 1 = h^2 + 3h + 3$ $f(2) = 2^2 - 2 + 1 = 3$ Now, we can substitute these into the difference quotient: Show more…
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In Exercises $87-92,$ find the difference quotient and simplify your answer. $$ f(x)=x^{3}+x, \quad \frac{f(x+h)-f(x)}{h}, \quad h \neq 0 $$
In Exercises $87-92,$ find the difference quotient and simplify your answer. $$ f(x)=2 x, \quad \frac{f(x+c)-f(x)}{c}, \quad c \neq 0 $$
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