/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 11 Suppose聽f1=3,聽limx鈫�1-fx=3,聽... [FREE SOLUTION] | 91影视

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Chapter 2: Q. 11 (page 183)

Supposef1=3,limx鈫�1-fx=3,limx鈫�1+fx=3,role="math" localid="1648483351627" limx鈫�0-f1+h-f1h=2,limx鈫�0+f1+h-f1h=0

(a) Is fcontinuous and/or differentiable at x=0? What

about from the left or right?

(b) Sketch a possible graph of f.

Short Answer

Expert verified

The function fis continuous but not differentiable at x=1.

The possible graph can be as follow:

Step by step solution

01

Step 1. Given information

It is given thatf1=3,limx鈫�1-fx=3,limx鈫�1+fx=3,limh鈫�0-f1+h-f1h=2,limh鈫�0+f1+h-f1h=0

02

Step 2. Check continuity and differentiability at x=1

Since f1=3, limx鈫�1-fx=3, limx鈫�1+fx=3, therefore the function is continuous at x=1.

limh鈫�0-f1+h-f1h=2and limh鈫�0+f1+h-f1h=0

Left hand derivatives and Right hand derivatives are not equal, So the function is not differentiable atx=1.

03

Step 3. Draw the possible graph of f.

The possible function will be

fx=3,ifx鈮�02x+1,ifx<0

So, the graph will be

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Most popular questions from this chapter

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=3x+1x2+1

Velocity v(t) is the derivative of position s(t). It is also true that acceleration a(t) (the rate of change of velocity) is the derivative of velocity. If a race car鈥檚 position in miles t hours after the start of a race is given by the function s(t), what are the units of s(1.2)? What are the units and real-world interpretation of v(1.2)? What are the units and real-world interpretations of a(1.2)?

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f(x)=x+45

Use the definition of the derivative to find f'for each function fin Exercises 34-59

role="math" localid="1648284617718" f(x)=2x+1

Each graph in Exercises 31鈥�34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

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