QuestionFind the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=7x+7$ . We are asked to find the difference quotient, which is $\frac{f(x+h)-f(x)}{h}$ , where $h \neq0$

STEP 2

First, we need to find $f(x+h)$ . We can do this by replacing $x$ with $(x+h)$ in the function.
$f(x+h) =7(x+h) +7$

STEP 3

Now, simplify the expression for $f(x+h)$ .
$f(x+h) =7x +7h +7$

STEP 4

Now, we need to find $f(x+h)-f(x)$ . We can do this by subtracting $f(x)$ from $f(x+h)$ .
$f(x+h)-f(x) = (7x +7h +7) - (7x +7)$

STEP 5

implify the expression for $f(x+h)-f(x)$ .
$f(x+h)-f(x) =7h$

STEP 6

Now, we can find the difference quotient by dividing $f(x+h)-f(x)$ by $h$ .
$\frac{f(x+h)-f(x)}{h} = \frac{h}{h}$

STEP 7

implify the difference quotient by cancelling out $h$ .
$\frac{f(x+h)-f(x)}{h} =7$ The difference quotient of the function $f(x)=7x+7$ is7.

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QuestionFind the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=7x+7$ . We are asked to find the difference quotient, which is $\frac{f(x+h)-f(x)}{h}$ , where $h \neq0$

STEP 2

First, we need to find $f(x+h)$ . We can do this by replacing $x$ with $(x+h)$ in the function.
$f(x+h) =7(x+h) +7$

STEP 3

Now, simplify the expression for $f(x+h)$ .
$f(x+h) =7x +7h +7$

STEP 4

Now, we need to find $f(x+h)-f(x)$ . We can do this by subtracting $f(x)$ from $f(x+h)$ .
$f(x+h)-f(x) = (7x +7h +7) - (7x +7)$

STEP 5

implify the expression for $f(x+h)-f(x)$ .
$f(x+h)-f(x) =7h$

STEP 6

Now, we can find the difference quotient by dividing $f(x+h)-f(x)$ by $h$ .
$\frac{f(x+h)-f(x)}{h} = \frac{h}{h}$

STEP 7

implify the difference quotient by cancelling out $h$ .
$\frac{f(x+h)-f(x)}{h} =7$ The difference quotient of the function $f(x)=7x+7$ is7.

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QuestionFind the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=7x+7f(x)=7x+7f(x)=7x+7, where h≠0h \neq 0h=0. Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=7x+7f(x)=7x+7f(x)=7x+7 . We are asked to find the difference quotient, which is f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​, where h≠0h \neq0h=0

STEP 2

First, we need to find f(x+h)f(x+h)f(x+h). We can do this by replacing xxx with (x+h)(x+h)(x+h) in the function.f(x+h)=7(x+h)+7f(x+h) =7(x+h) +7f(x+h)=7(x+h)+7

STEP 3

Now, simplify the expression for f(x+h)f(x+h)f(x+h).f(x+h)=7x+7h+7f(x+h) =7x +7h +7f(x+h)=7x+7h+7

STEP 4

Now, we need to find f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x). We can do this by subtracting f(x)f(x)f(x) from f(x+h)f(x+h)f(x+h).f(x+h)−f(x)=(7x+7h+7)−(7x+7)f(x+h)-f(x) = (7x +7h +7) - (7x +7)f(x+h)−f(x)=(7x+7h+7)−(7x+7)

STEP 5

implify the expression for f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x).f(x+h)−f(x)=7hf(x+h)-f(x) =7hf(x+h)−f(x)=7h

STEP 6

Now, we can find the difference quotient by dividing f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x) by hhh.f(x+h)−f(x)h=hh\frac{f(x+h)-f(x)}{h} = \frac{h}{h}hf(x+h)−f(x)​=hh​

STEP 7

implify the difference quotient by cancelling out hhh.f(x+h)−f(x)h=7\frac{f(x+h)-f(x)}{h} =7hf(x+h)−f(x)​=7The difference quotient of the function f(x)=7x+7f(x)=7x+7f(x)=7x+7 is7.

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QuestionFind the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

Assumptions1. The function is $f(x)=7x+7$ . We are asked to find the difference quotient, which is $\frac{f(x+h)-f(x)}{h}$ , where $h \neq0$

First, we need to find $f(x+h)$ . We can do this by replacing $x$ with $(x+h)$ in the function.
$f(x+h) =7(x+h) +7$

Now, simplify the expression for $f(x+h)$ .
$f(x+h) =7x +7h +7$

Now, we need to find $f(x+h)-f(x)$ . We can do this by subtracting $f(x)$ from $f(x+h)$ .
$f(x+h)-f(x) = (7x +7h +7) - (7x +7)$

implify the expression for $f(x+h)-f(x)$ .
$f(x+h)-f(x) =7h$

Now, we can find the difference quotient by dividing $f(x+h)-f(x)$ by $h$ .
$\frac{f(x+h)-f(x)}{h} = \frac{h}{h}$

implify the difference quotient by cancelling out $h$ .
$\frac{f(x+h)-f(x)}{h} =7$ The difference quotient of the function $f(x)=7x+7$ is7.