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anonymous
 one year ago
Use the following three steps to find and simplify the difference quotient of the function
f(x)=\frac{1}{x6}.
anonymous
 one year ago
Use the following three steps to find and simplify the difference quotient of the function f(x)=\frac{1}{x6}.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I believe I do the correct work but for the last two steps it says I am wrong.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The difference quotient: \(\dfrac{f(x+h)f(x)}{h}\) So let's begin by finding \(f(x+h)\) first. Wherever you see an x, replace it with \(x+h\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then i'm suppose to subtract it by f(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, now we plug it in to the formula. And you are already given \(f(x)\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01/(x+h)6  1/x = h6/x(x+h)6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{f(x+h)f(x)}{h} = \frac{\dfrac{1}{x+h6}\dfrac{1}{x6}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When I find a common denominator, I multiply both the denominators of the fraction together.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[=\frac{\dfrac{x6 (x+h6)}{(x6)(x+h6)}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now let's simplify both the numerator and denominator.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0isn't the top suppose to be h

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then h/(x+h6)(x6)/h

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, you're on track. That's what I got too. \[=\frac{\dfrac{x6xh+6}{(x6)(x+h6)}}{h} = \frac{\dfrac{h}{(x6)(x+h6)}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now remember the rule of dividing fractions? \(\dfrac{\dfrac{a}{b}}{c} \iff \dfrac{a}{bc}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its h^2/(x+h6)(x6)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We're going to apply this rule to our simplified function. We multiply \((x6)(x+h6)\) with \(h\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ \frac{\dfrac{h}{(x6)(x+h6)}}{h} = \frac{h}{h(x6)(x+h6)}\]Therefore both the h's cancel out.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{\cancel{h}}{\cancel{h}(x6)(x+h6)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it says the bottom is not correct

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when you think of a fraction in the form \(\dfrac{\dfrac{a}{b}}{c}\) think of \(\dfrac{a}{b} \cdot \dfrac{1}{c} = \dfrac{a}{bc} \)
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