Find the Linearization at x=6

$f (x) = x + 7$ , $x = 6$

Step 1

Consider the function used to find the linearization at $a$ .

$L (x) = f (a) + f' (a) (x - a)$

Step 2

Substitute the value of $a = 6$ into the linearization function.

$L (x) = f (6) + f' (6) (x - 6)$

Step 3

Evaluate $f (6)$ .

Tap for more steps...

Step 3.1

Replace the variable $x$ with $6$ in the expression.

$f (6) = (6) + 7$

Step 3.2

Simplify $(6) + 7$ .

Tap for more steps...

Step 3.2.1

Remove parentheses.

$(6) + 7$

Step 3.2.2

Add $6$ and $7$ .

$13$

Step 4

Find the derivative of $f (x) = x + 7$ .

Tap for more steps...

Step 4.1

By the Sum Rule, the derivative of $x + 7$ with respect to $x$ is $\frac{d}{d x} [x] + \frac{d}{d x} [7]$ .

$\frac{d}{d x} [x] + \frac{d}{d x} [7]$

Step 4.2

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

$1 + \frac{d}{d x} [7]$

Step 4.3

Since $7$ is constant with respect to $x$ , the derivative of $7$ with respect to $x$ is $0$ .

$1 + 0$

Step 4.4

Add $1$ and $0$ .

$1$

Step 5

Substitute the components into the linearization function in order to find the linearization at $a$ .

$L (x) = 13 + 1 (x - 6)$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Multiply $x - 6$ by $1$ .

$L (x) = 13 + x - 6$

Step 6.2

Subtract $6$ from $13$ .

$L (x) = x + 7$

Step 7

Enter YOUR Problem

How to Use Step-by-Step Examples

Read the worked problem

Each example starts from a real Calculus problem and shows the rule or formula it relies on.

Follow every step

Work through the solution line by line. Underlined terms open a glossary definition.

Solve your own problem

Enter a similar problem in the Calculus solver to get the answer with steps.

Why use Mathway?

Step-by-step solutions

See how every answer is worked out, not just the result.

Every major math subject

From basic math through calculus, statistics and chemistry.

Accurate results

Answers you can check your homework against.

Trusted by students

A reliable tool for homework and learning.

Find the Linearization at x=6

Derivatives

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Calculus Help