IXL - Find instantaneous rates of change (Calculus 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

The function

(

)

is a constant linear function. The graph of any constant linear function is a horizontal line.

Since

(

)

takes on only one value, 3, it never changes. So, the instantaneous rate of change is 0, which is the slope of a horizontal line.

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:

F.2Average rate of change II

B.6Find limits involving factorization and rationalization

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