IXL - Find equations of tangent lines using limits (Calculus 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
(
–
7
,
k
(
–
7
)
)
and
has slope equal to
k
′
(
–
7
)
.

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

–

Write the equation of the tangent line.

The tangent line goes through the point

(

–

)

and has slope

–

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

–

(

–

)

–

Plug in

–

(

–

)

Plug in

–

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

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

L.15Point-slope form: write an equation

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!