IXL - Find equations of tangent lines using limits (Precalculus practice)

Find the equation of the tangent line to

(

)

Write your answer in point-slope form using integers and fractions. Simplify any fractions.

–

ref_doc_title.

Learn with an example

question

Find the equation of the tangent line to

(

)

Write your answer in point-slope form using integers and fractions. Simplify any fractions.

–

key idea

The tangent line to

(

)

is a line that

passes through
(
a
,
g
(
a
)
)
and
has slope equal to
g
′
(
a
)
.

The slope of the tangent line,

′

(

)

is also called the derivative of

(

)

It is defined by the following formula:

′

(

)

lim

→0

(

)

–

(

)

The equation of a line in point-slope form is

–

(

–

)

where

(

)

is a point on the line, and

is the slope.

solution

The tangent line to

(

)

is a line that

passes through
(
2
,
k
(
2
)
)
and
has slope equal to
k
′
(
2
)
.

Find

(

)

Find the point

(

)

on the tangent line by evaluating

(

)

(

)

So,

(

)

is a point on the line.

Find

′

(

)

Find the slope of the tangent line by evaluating

′

(

)

′

(

)

lim

→0

(

)

–

(

)

lim

→0

(

)

–

(

)

lim

→0

(

)

–

lim

→0

lim

→0

(

)

Cancel

lim

→0

(

)

Cancel

The slope is 4.

Write the equation of the tangent line.

The tangent line goes through the point

(

)

and has slope 4. You can use point-slope form to write the equation.

–

(

–

)

–

Plug in

(

–

)

Plug in

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Work it out

Not feeling ready yet? These can help:

JJ.6Find the slope of a tangent line using limits

L.15Point-slope form: write an equation

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