Chapter 14: Q. 21 (page 897)

In Problems 21–32, find the derivative of each function at the given number.
$f (x) = - 4 x + 5$ at $3$

Short Answer

Expert verified

The derivative of given function at $x = 3$ is $- 4$ .

Step by step solution

Step 1. Given Information

We are given a function,

$f (x) = - 4 x + 5$

We have to find the derivative of the given function at $3$ .

Step 2. Definition of derivative

The derivative of the function at c is defined as,

$f' (c) = \lim_{x \to c} \frac{f (x) - f (c)}{x - c}$

Here, $c = 3$

$f (x) = - 4 x + 5 f (3) = - 4 (3) + 5 = - 12 + 5 = - 7$

Step 3. Finding the derivative

By substituting the given function in the derivative definition, we get

$f' (3) = \lim_{x \to 3} \frac{f (x) - f (3)}{x - 3} = \lim_{x \to 3} \frac{- 4 x + 5 - (- 7)}{x - 3} = \lim_{x \to 3} \frac{- 4 x + 12}{x - 3} = \lim_{x \to 3} \frac{- 4 (x - 3)}{x - 3} = \lim_{x \to 3} - 4 = - 4$

Hence, the derivative of the function is $- 4$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 21–32, find the derivative of each function at the given number.
$f (x) = - 4 x + 5$ at $3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Definition of derivative

Step 3. Finding the derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Decision Maths

Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 21–32, find the derivative of each function at the given number.f(x)=-4x+5at3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Definition of derivative

Step 3. Finding the derivative

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Decision Maths

Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 21–32, find the derivative of each function at the given number.
$f (x) = - 4 x + 5$ at $3$