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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.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1The 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)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Alright, 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

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1When I find a common denominator, I multiply both the denominators of the fraction together.

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Now 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Yep, you're on track. That's what I got too. \[=\frac{\dfrac{x6xh+6}{(x6)(x+h6)}}{h} = \frac{\dfrac{h}{(x6)(x+h6)}}{h}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Now 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)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1We're going to apply this rule to our simplified function. We multiply \((x6)(x+h6)\) with \(h\).

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{\dfrac{h}{(x6)(x+h6)}}{h} = \frac{h}{h(x6)(x+h6)}\]Therefore both the h's cancel out.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{\cancel{h}}{\cancel{h}(x6)(x+h6)}\]

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1when 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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