Explanation Given: f ( x ) = m x + b Concept Used: According to definition of derivative of a function f ( x ) , the derivative of a function f ( x ) is given by: f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Domain of a function is set of all the points where it is define. Calculation: To find derivative of the function f ( x ) = m x + b Use the definition of derivative which states f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Thus, derivative of given function can be calculated as f ′ ( x ) =

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.2, Problem 22E

To determine

To find the derivative of the function

f(x)=mx+b

Also find the domain of the function and the domain of its derivative.

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Chapter 3.2, Problem 21E

Chapter 3.2, Problem 23E

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8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

8:39 *** TEMU 5G 60% A ferris wheel is 28 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude? 14 meters What is the equation of the Midline? y = 16 What is the period? 4 meters minutes The equation that models the height of the ferris wheel after t minutes is: f(t): = ƒ (3) = ·−14(0) + 16 syntax error: you gave an equation, not an expression. syntax error. Check your variables - you might be using an incorrect one. How high are you off of the ground after 3 minutes? Round your answe the nearest meter. ||| <

Chapter 3 Solutions

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To find the derivative of the function f ( x ) = m x + b Also find the domain of the function and the domain of its derivative.

Solution Summary: The author explains how to find the derivative of the function f(x)=mx+b and its domain.

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To find the derivative of the function

f(x)=mx+b

Also find the domain of the function and the domain of its derivative.

Want to see the full answer?

Chapter 3 Solutions

To find the derivative of the function f ( x ) = m x + b Also find the domain of the function and the domain of its derivative.

Solution Summary: The author explains how to find the derivative of the function f(x)=mx+b and its domain.

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To find the derivative of the function f(x)=mx+b Also find the domain of the function and the domain of its derivative.

Want to see the full answer?

Chapter 3 Solutions

To find the derivative of the function

f(x)=mx+b

Also find the domain of the function and the domain of its derivative.