Question

Let $f(x)=17 x+11 .$ Use the definition of the derivative to calculate $f^{\prime}(x)$.

Name: Problem 2, Chapter 3: Calculus Single Variable
Uploaded: 2021-04-15T12:43:44-08:00
Duration: 1 min 46 s
Channel: Gregory Higby
Description: Let f(x)=17 x+11 . Use the definition of the derivative to calculate f^'(x).

   Let $f(x)=17 x+11 .$ Use the definition of the derivative to calculate $f^{\prime}(x)$.

Calculus Single Variable

Deborah… 7th Edition

Chapter 3, Problem 2

Instant Answer

Solved by Expert Gregory Higby

04/15/2021

Step 1

Step 1: The definition of the derivative is given by the limit: \[f^{\prime}(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\] Show more…

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Let $f(x)=17 x+11 .$ Use the definition of the derivative to calculate $f^{\prime}(x)$.

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Key Concepts

Definition of the Derivative

The derivative of a function is defined as the limit of the difference quotient as the increment approaches zero. This limit represents the instantaneous rate of change of the function with respect to its variable and forms a fundamental concept in differential calculus.

Difference Quotient

The difference quotient, given by [f(x + h) - f(x)]/h, is an expression used to approximate the derivative of a function over an interval of length h. By taking the limit as h approaches zero, one obtains the precise derivative, capturing the idea of a function's instantaneous change.

Properties of Linear Functions

Linear functions, which are in the form f(x) = mx + b, have a constant rate of change. This property is evident when using the derivative definition, as the derivative of a linear function consistently equals the coefficient m, reflecting its constant slope throughout its domain.

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