Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Essential Calculus: Early Transcendentals
Found in: Page 208
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Sketch the graph of a function that is continuous on (1, 5) and has the given properties.

8. Absolute minimum at 1, absolute maximum at 5, local maximum at 2, local minimum at 4.

The graph is sketched.

See the step by step solution

Step by Step Solution

Step 1: Given data

The given function is the value of absolute minimum is at 1, absolute maximum is at 5, local maximum at 2, local minimum at 4.

Step 2: Concept of Differentiation

Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.

Step 3: Sketch the graph

To keep it simple, I will use straight line segments to draw the graph. It is not given that \(f\) is differentiable everywhere, so its graph need not be smooth at all points. Note that: If the absolute minimum/maximum are not the endpoints of the domain and the function is continuous (as the case here), they are also the local minimum/maximum, respectively.

It is not necessary to draw the dashed vertical lines at \(x = 1,5\). I am drawing them to show that the function is defined between (and on the) two boundaries. The graph of the given function is:

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.