,

Consider the function used to find the linearization at .

Substitute the value of into the linearization function.

Replace the variable with in the expression.

Simplify .

Remove parentheses.

Remove parentheses.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Find the derivative of .

Use to rewrite as .

Differentiate using the Power Rule which states that is where .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Rewrite the expression using the negative exponent rule .

Multiply and .

Replace the variable with in the expression.

Simplify.

Simplify the denominator.

Rewrite as .

Apply the power rule and multiply exponents, .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Multiply by .

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

Simplify each term.

Apply the distributive property.

Combine and .

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Write in form.

Find the Linearization at a=9 f(x) = square root of x , a=9