Calculus Examples

$y = x - 2$

Step 1

Set $y$ as a function of $x$ .

$f (x) = x - 2$

Step 2

Find the derivative.

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Step 2.1

By the Sum Rule, the derivative of $x - 2$ with respect to $x$ is $\frac{d}{d x} [x] + \frac{d}{d x} [- 2]$ .

$\frac{d}{d x} [x] + \frac{d}{d x} [- 2]$

Step 2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$1 + \frac{d}{d x} [- 2]$

Step 2.3

Since $- 2$ is constant with respect to $x$ , the derivative of $- 2$ with respect to $x$ is $0$ .

$1 + 0$

Step 2.4

Add $1$ and $0$ .

$1$

Step 3

Since $1 \neq 0$ , there are no solutions.

No solution

Step 4

There are no solution found by setting the derivative equal to $0$ , $1 = 0$ so there are no horizontal tangent lines.

No horizontal tangent lines found

Step 5