Q. 86 In Exercises 83鈥�86, use the gi... [FREE SOLUTION]

91影视

Chapter 10: Q. 86 (page 777)

In Exercises 83鈥�86, use the given derivative f' to find any local extrema and inflection points of f and sketch a possible graph without first finding an formula for f .
$f' (x) = e^{x} (x + 4)$

Short Answer

Expert verified

A critical point is $x = - 4$

Step by step solution

Given information

The function's name is $f' (x) = e^{x} (x + 4)$

Calculations

Consider the following factors while determining the important points:

$\begin{matrix} f' (x) = 0 \\ e^{x} (x + 4) = 0 \\ \begin{array}{rcl} (x + 4) & = & 0 \\ x & = & 4 \end{array} \end{matrix}$

As a result, A critical point is $x = - 4$

Then take a look at the table below.

Interval	$(鈭� 鈭�, 鈭� 4)$	$(鈭� 4, 鈭�)$
k	-5	0
Value of the test for $f' (k)$	-	+
sign of $f' (x)$	$f^{鈥�} (x) < 0$	$f^{鈥�} (x) > 0$
Conclusion	Decreasing	Increasing

Therefore, The crucial point is $x = - 4$ .

Then there's the graph of f,

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Exercises 83鈥�86, use the given derivative f' to find any local extrema and inflection points of f and sketch a possible graph without first finding an formula for f .
$f' (x) = e^{x} (x + 4)$

Short Answer

Step by step solution

Given information

Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Logic and Functions

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

91影视

In Exercises 83鈥�86, use the given derivative f' to find any local extrema and inflection points of f and sketch a possible graph without first finding an formula for f .f'x=exx+4

Short Answer

Step by step solution

Given information

Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Logic and Functions

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 83鈥�86, use the given derivative f' to find any local extrema and inflection points of f and sketch a possible graph without first finding an formula for f .
$f' (x) = e^{x} (x + 4)$