Calculus Examples

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

Step 1

Insert the values of $x = 2$ and $y = 2$ into the equation to find if the ordered pair is a solution.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $2$ to the power of $3$ .

$2 = 8 - 3 \cdot 2$

Step 2.1.2

Multiply $- 3$ by $2$ .

$2 = 8 - 6$

Step 2.2

Subtract $6$ from $8$ .

$2 = 2$

Step 3

Since $2 = 2$ , 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.