Math  /  Calculus

QuestionFind the difference quotient of f(x)=1x+2f(x)=\frac{1}{x+2} and simplify.

Studdy Solution
The hh in the numerator and denominator cancel out, leaving us with the simplified difference quotient.
f(x+h)f(x)h=1(x+h+2)(x+2)\frac{f(x+h)-f(x)}{h} = \frac{-1}{(x+h+2)(x+2)}So, the difference quotient of f(x)=1x+2f(x)=\frac{1}{x+2} is 1(x+h+2)(x+2)\frac{-1}{(x+h+2)(x+2)}.

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