Asked by Monique
Find the difference quotient for the following Rational Function f(x)=5/x using the four steps outlined below.
a. find f(x+h)
b. find f(x)
c. substitute f(x+h) and f(x) into the difference quotient formula.
d. simplify
a. find f(x+h)
b. find f(x)
c. substitute f(x+h) and f(x) into the difference quotient formula.
d. simplify
Answers
Answered by
Damon
f(x+h) = 5/(x+h)
f(x) = 5/x
[f(x+h) - f(x)]/h = [5x -5(x+h)]/[hx(x+h)]
= -5 /[x(x+h) }
= -5/(x^2+hx)
By the way,
if you take the limit of that as h--->0
then you are a calculus student and you just found the derivative
d/dx (5/x) = -5/x^2
f(x) = 5/x
[f(x+h) - f(x)]/h = [5x -5(x+h)]/[hx(x+h)]
= -5 /[x(x+h) }
= -5/(x^2+hx)
By the way,
if you take the limit of that as h--->0
then you are a calculus student and you just found the derivative
d/dx (5/x) = -5/x^2
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