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Find the instantaneous rate of change of $k(x) = x$ at $x = 13$ . $\newline$ Write your answer as an integer or a fractions" target="_blank" class="backlink">fraction. Simplify any fractions. $\newline$ ____ $\newline$

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Find instantaneous rates of change

Full solution

Q. Find the instantaneous rate of change of

k(x) = x

at

x = 13

.

\newline

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

\newline

____

\newline

Identify function and point: Identify the function and the point where the rate of change is needed. $\newline$ Function: $k(x) = x$ $\newline$ Point: $x = 13$
Recognize derivative as rate of change: Recognize that the derivative of $k(x) = x$ is the instantaneous rate of change. $\newline$ Derivative of $k(x) = 1$ (since the derivative of $x$ with respect to $x$ is $1$ ).
Evaluate derivative at $x = 13$ : Evaluate the derivative at $x = 13$ . $\newline$ Since the derivative is $1$ , the value at $x = 13$ is also $1$ .

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