IXL - Find the slope of a tangent line using limits (Precalculus practice)

Find the slope of the tangent line to

(

)

–

Write your answer as an integer or a fraction. Simplify any fractions.

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question

Find the slope of the tangent line to

(

)

–

Write your answer as an integer or a fraction. Simplify any fractions.

key idea

The slope of the tangent line to

(

)

is:

lim

→0

(

)

–

(

)

This limit is also called the derivative of

(

)

and it is written

′

(

)

It is the instantaneous rate of change of

(

)

When

(

)

is a linear function, all of its tangent lines are the same as the graph of

(

)

solution

The graph of

(

)

is a horizontal line. The tangent line is the same horizontal line.

Since all horizontal lines have a slope of 0, the slope of the tangent line is 0.

You can also find the slope of the tangent line to

(

)

–

using the limit definition.

lim

→0

(

–

)

–

(

–

)

You cannot simply plug in

to evaluate the limit, because doing so makes the denominator 0. You must first simplify the numerator and cancel the

in the denominator.

lim

→0

(

–

)

–

(

–

)

lim

→0

–

lim

→0

Cancel

lim

→0

Cancel

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