IXL - Linear approximation (Calculus practice)

Find the linearization of

(

)

Write an exact answer.

(

)

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Learn with an example

question

Find the linearization of

(

)

–

Write an exact answer.

(

)

key idea

You can use tangent lines to approximate values of differentiable functions. This is the equation of the line tangent to the graph

(

)

(

)

(

)

′

(

)

(

–

)

(

)

is known as the

linearization,

or linear

approximation,

(

)

For values of

near

(

)

is a good approximation for

(

)

solution

To find the linearization of

(

)

–

you can use the equation

(

)

(

)

′

(

)

(

–

)

with

So, you need to find

(

)

and

′

(

)

(

)

–

(

)

–

To find

′

(

)

take the derivative of

(

)

and plug in

(

)

–

′

(

)

–

′

(

)

(

)

–

(

)

(

)

–

(

)

–

Finally, write the equation for

(

)

Plug in the values for

(

)

and

′

(

)

(

)

(

)

′

(

)

(

–

)

(

)

′

(

)

(

–

)

(

–

)

–

So,

(

)

–

is the linearization of

(

)

–

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Not feeling ready yet? These can help:

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