IXL - Find instantaneous rates of change (Precalculus practice)

Find the instantaneous rate of change of

(

)

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

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question

Find the instantaneous rate of change of

(

)

–

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

key idea

The instantaneous rate of change of a function

(

)

is:

lim

→0

(

)

–

(

)

This limit is also called the derivative of

(

)

and it is written

′

(

)

It is the slope of the tangent line to

(

)

at the point

(

)

When

(

)

is a linear function, the instantaneous rate of change is always equal to the slope.

solution

Since

(

)

is a linear function with slope 1, the instantaneous rate of change is 1.

You can also find the instantaneous rate of change of

(

)

–

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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Not feeling ready yet? These can help:

JJ.2Average rate of change II

HH.11Find limits involving factorization and rationalization

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