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Chapter 3: Q. 10 (page 260)

Sketch the graph of a function f with the following properties:

f is continuous and defined on R;

f has critical points at x = 鈭�3, 0, and 5;

f has inflection points at x = 鈭�3, 鈭�1, and 2.

Short Answer

Expert verified

Graph is :

Step by step solution

01

Step 1. Given information 

We have been given the following properties of a function f:

f is continuous and defined on R;

f has critical points at x = 鈭�3, 0, and 5;

f has inflection points at x = 鈭�3, 鈭�1, and 2.

We have to sketch the graph of this function.

02

Step 2. Sketch the graph

For critical points :

f鈥�(鈭�3)=0;f鈥�(0)=0;f鈥�(5)=0

For inflection points :

f鈥测赌�(鈭�3)=0;f鈥测赌�(鈭�1)=0;f鈥测赌�(2)=0

Thus, the graph is:

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Most popular questions from this chapter

Sketch the graph of a function f with the following properties:

f is continuous and defined on R;

f(0) = 5;

f(鈭�2) = 鈭�3 and f '(鈭�2) = 0;

f '(1) does not exist;

f' is positive only on (鈭�2, 1).

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=x3鈭�2x2+x

Find the possibility graph of its derivative f'.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=cosx

Determine whether or not each function f in Exercises 53鈥�60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=x2+1x,[a,b]=[鈭�3,2]
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