Finite Math Examples

$p = - \frac{1}{10} x + 1860$ , $C (x) = 140 x + 3000$

Step 1

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 2

Find the components of the definition.

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Step 2.1

Evaluate the function at $x = x + h$ .

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Step 2.1.1

Replace the variable $x$ with $x + h$ in the expression.

$C (x + h) = 140 (x + h) + 3000$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Apply the distributive property.

$C (x + h) = 140 x + 140 h + 3000$

Step 2.1.2.2

The final answer is $140 x + 140 h + 3000$ .

$140 x + 140 h + 3000$

Step 2.2

Reorder $140 x$ and $140 h$ .

$140 h + 140 x + 3000$

Step 2.3

Find the components of the definition.

$C (x + h) = 140 h + 140 x + 3000$

$C (x) = 140 x + 3000$

$C (x + h) = 140 h + 140 x + 3000$

$C (x) = 140 x + 3000$

Step 3

Plug in the components.

$\frac{C (x + h) - C x}{h} = \frac{140 h + 140 x + 3000 - (140 x + 3000)}{h}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $20$ out of $140 x + 3000$ .

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Step 4.1.1.1

Factor $20$ out of $140 x$ .

$\frac{140 h + 140 x + 3000 - (20 (7 x) + 3000)}{h}$

Step 4.1.1.2

Factor $20$ out of $3000$ .

$\frac{140 h + 140 x + 3000 - (20 (7 x) + 20 (150))}{h}$

Step 4.1.1.3

Factor $20$ out of $20 (7 x) + 20 (150)$ .

$\frac{140 h + 140 x + 3000 - (20 (7 x + 150))}{h}$

$\frac{140 h + 140 x + 3000 - 1 \cdot 20 (7 x + 150)}{h}$

Step 4.1.2

Multiply $- 1$ by $20$ .

$\frac{140 h + 140 x + 3000 - 20 (7 x + 150)}{h}$

Step 4.1.3

Factor $20$ out of $140 h + 140 x + 3000 - 20 (7 x + 150)$ .

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Step 4.1.3.1

Factor $20$ out of $140 h$ .

$\frac{20 (7 h) + 140 x + 3000 - 20 (7 x + 150)}{h}$

Step 4.1.3.2

Factor $20$ out of $140 x$ .

$\frac{20 (7 h) + 20 (7 x) + 3000 - 20 (7 x + 150)}{h}$

Step 4.1.3.3

Factor $20$ out of $3000$ .

$\frac{20 (7 h) + 20 (7 x) + 20 (150) - 20 (7 x + 150)}{h}$

Step 4.1.3.4

Factor $20$ out of $- 20 (7 x + 150)$ .

$\frac{20 (7 h) + 20 (7 x) + 20 (150) + 20 (- (7 x + 150))}{h}$

Step 4.1.3.5

Factor $20$ out of $20 (7 h) + 20 (7 x)$ .

$\frac{20 (7 h + 7 x) + 20 (150) + 20 (- (7 x + 150))}{h}$

Step 4.1.3.6

Factor $20$ out of $20 (7 h + 7 x) + 20 (150)$ .

$\frac{20 (7 h + 7 x + 150) + 20 (- (7 x + 150))}{h}$

Step 4.1.3.7

Factor $20$ out of $20 (7 h + 7 x + 150) + 20 (- (7 x + 150))$ .

$\frac{20 (7 h + 7 x + 150 - (7 x + 150))}{h}$

Step 4.1.4

Apply the distributive property.

$\frac{20 (7 h + 7 x + 150 - (7 x) - 1 \cdot 150)}{h}$

Step 4.1.5

Multiply $7$ by $- 1$ .

$\frac{20 (7 h + 7 x + 150 - 7 x - 1 \cdot 150)}{h}$

Step 4.1.6

Multiply $- 1$ by $150$ .

$\frac{20 (7 h + 7 x + 150 - 7 x - 150)}{h}$

Step 4.1.7

Subtract $7 x$ from $7 x$ .

$\frac{20 (7 h + 0 + 150 - 150)}{h}$

Step 4.1.8

Add $7 h$ and $0$ .

$\frac{20 (7 h + 150 - 150)}{h}$

Step 4.1.9

Subtract $150$ from $150$ .

$\frac{20 (7 h + 0)}{h}$

Step 4.1.10

Add $7 h$ and $0$ .

$\frac{20 \cdot 7 h}{h}$

Step 4.1.11

Multiply $20$ by $7$ .

$\frac{140 h}{h}$

Step 4.2

Cancel the common factor of $h$ .

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Step 4.2.1

Cancel the common factor.

$\frac{140 h}{h}$

Step 4.2.2

Divide $140$ by $1$ .

$140$

Step 5