Question

Solve the given problems by finding the appropriate derivative. The electric power $P$ (in $\mathrm{W}$ ) as a function of the current $i$ (in $\mathrm{A}$ ) in a certain circuit is given by $P=16 i^{2}+60 i .$ Find the instantaneous rate of change of $P$ with respect to $i$ for $i=0.75 A$.

Name: Problem 47, Chapter 23: Basic Technical Mathematics with Calculus
Uploaded: 2021-06-06T13:25:46-08:00
Duration: 3 min 9 s
Channel: Barsha Rana
Description: Solve the given problems by finding the appropriate derivative. The electric power P (in W ) as a function of the current i (in A ) in a certain circuit is given by P=16 i^2+60 i . Find the instantaneous rate of change of P with respect to i for i=0.75 A.

   Solve the given problems by finding the appropriate derivative.
The electric power $P$ (in $\mathrm{W}$ ) as a function of the current $i$ (in $\mathrm{A}$ ) in a certain circuit is given by $P=16 i^{2}+60 i .$ Find the instantaneous rate of change of $P$ with respect to $i$ for $i=0.75 A$.

Basic Technical Mathematics with Calculus

Allyn J. Washington,… 11th Edition

Chapter 23, Problem 47

Instant Answer

Solved by Expert Barsha Rana

06/06/2021

Step 1

We need to find the instantaneous rate of change of $P$ with respect to $i$ for $i=0.75 A$. This is equivalent to finding the derivative of $P$ with respect to $i$ at $i=0.75 A$. Show more…

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Solve the given problems by finding the appropriate derivative. The electric power $P$ (in $\mathrm{W}$ ) as a function of the current $i$ (in $\mathrm{A}$ ) in a certain circuit is given by $P=16 i^{2}+60 i .$ Find the instantaneous rate of change of $P$ with respect to $i$ for $i=0.75 A$.

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Key Concepts

Evaluation of Derivatives

Evaluating a derivative involves substituting a specific value of the independent variable into the derivative expression. This computation provides the exact rate of change of the function at that point.

Instantaneous Rate of Change

The instantaneous rate of change is the value of the derivative at a particular point on the function. It represents how quickly the function is changing at that specific instant.

Derivative

The derivative of a function is a measure of its instantaneous rate of change with respect to one of its independent variables. It tells us the slope of the tangent line to the function at any given point and is a cornerstone concept in calculus.

Power Rule

The power rule is a basic method used in differentiation, which states that the derivative of a term in the form ax^n is a*n*x^(n-1). This rule simplifies the process of differentiating polynomial functions.

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