Calculus Examples

$y = 3 x^{3} - 2 x$ , $(1, 1)$

Step 1

Insert the values of $x = 1$ and $y = 1$ into the equation to find if the ordered pair is a solution.

$1 = 3 {(1)}^{3} - 2 \cdot 1$

Step 2

Simplify $3 {(1)}^{3} - 2 \cdot 1$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

One to any power is one.

$1 = 3 \cdot 1 - 2 \cdot 1$

Step 2.1.2

Multiply $3$ by $1$ .

$1 = 3 - 2 \cdot 1$

Step 2.1.3

Multiply $- 2$ by $1$ .

$1 = 3 - 2$

Step 2.2

Subtract $2$ from $3$ .

$1 = 1$

Step 3

Since $1 = 1$ , the equation will always be true.

Always true

Step 4

Since the equation is always true when the values are used, the ordered pair is a solution.

The ordered pair is a solution to the equation.