   Chapter 2.2, Problem 56E

Chapter
Section
Textbook Problem

(a) If g ( x ) = x 2 / 3 , show that g ' ( 0 ) does not exist.(b) If a ≠ 0 , find g ' ( a ) .(c) Show that y = x 2 / 3 has a vertical tangent line at ( 0 , 0 ) .(d) Illustrate part (c) by graphing y = x 2 / 3 .

To determine

(a)

To show: g'0 does not exist

Explanation

As we know

g'a= limxagx-g(a)x-a

Given:

gx=x2/3

Calculation:

Here a=0

Thus ga=0=02/3

Now substitute all values in

g'a= limxagx-g(a)x-a

g'0= limx0x2/3-02/3x-0

g'0= lim

To determine

(b)

To find: g'a

To determine

(c)

To show: y=x23 has vertical tangent line at (0, 0)

To determine

(d)

To illustrate: part (c)

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