Chapter 4.3, Problem 96E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Electrical Resistance The resistance R of a certain type of resistor is R = 0.001 T 4 − 4 T + 100 where R is measured in ohms and the temperature I is measured in degrees Celsius.(a) Use a computer algebra system to find d R / d T and the critical number of the function. Determine the minimum resistance for this type of resistor.(b) Use a graphing utility to graph the function R and use the graph to approximate the minimum resistance for this type of resistor.

(a)

To determine

To calculate: The value of dRdT and thus the critical number and minima of the provided function, R=0.001T44T+100

Explanation

Given:

The formula for the resistance R in ohms across a resistor at temperature T degree Celsius is:

R=0.001T4âˆ’4T+100

Formula used:

The function f(x) is said to have a critical number c if f'(c)=0 or if f'(c) does not exist.

So, for a critical point c of a function f(x),

If the derivative of the function, f(x), changes sign from a negative value to a positive value at the point c, the f is said to have a relative minima at the point c.

If the derivative of the function, f(x), changes sign from a positive value to a negative value at the point c, the f is said to have a relative maxima at the point c.

If the derivative function does not change sign at the critical point, the point is neither a maxima nor a minima.

Calculation:

Use Maple to obtain the derivative of the function.

Maple command

The critical number can be computed by equating the derivative to zero and then solving for x.

dRdT=0

(b)

To determine

To graph: The provided function R=0.001T44T+100 and then to verify the minima obtained.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find the domain of the function. 5. f(x)=cosx1sinx

Single Variable Calculus: Early Transcendentals, Volume I

#### Sketch the graph of the line that passes through the point (3, 2) and has slope 23.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problem 8-10, solve the inequality and graph the solution

Mathematical Applications for the Management, Life, and Social Sciences

#### Solve: 42x=18

Elementary Technical Mathematics