Calculus Examples

$18 - 12 x$

Step 1

Find the first derivative.

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Step 1.1

Find the first derivative.

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Step 1.1.1

Differentiate.

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Step 1.1.1.1

By the Sum Rule, the derivative of $18 - 12 x$ with respect to $x$ is $\frac{d}{d x} [18] + \frac{d}{d x} [- 12 x]$ .

$\frac{d}{d x} [18] + \frac{d}{d x} [- 12 x]$

Step 1.1.1.2

Since $18$ is constant with respect to $x$ , the derivative of $18$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 12 x]$

Step 1.1.2

Evaluate $\frac{d}{d x} [- 12 x]$ .

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Step 1.1.2.1

Since $- 12$ is constant with respect to $x$ , the derivative of $- 12 x$ with respect to $x$ is $- 12 \frac{d}{d x} [x]$ .

$0 - 12 \frac{d}{d x} [x]$

Step 1.1.2.2

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

$0 - 12 \cdot 1$

Step 1.1.2.3

Multiply $- 12$ by $1$ .

$0 - 12$

Step 1.1.3

Subtract $12$ from $0$ .

$f' (x) = - 12$

Step 1.2

The first derivative of $f (x)$ with respect to $x$ is $- 12$ .

$- 12$

Step 2

Set the first derivative equal to $0$ then solve the equation $- 12 = 0$ .

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Step 2.1

Set the first derivative equal to $0$ .

$- 12 = 0$

Step 2.2

Since $- 12 \neq 0$ , there are no solutions.

No solution

Step 3

There are no values of $x$ in the domain of the original problem where the derivative is $0$ or undefined.

No critical points found