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Chapter 2: Q. 11 (page 165)

For the graph of f appearing next at the left, label each of the following quantities to illustrate that

f鈥�(c)鈮�f(c+h)鈭�f(c)h

(a) the locations c, c + h, f(c), and f(c + h)

(b) the distances h and f(c + h) 鈭� f(c)

(c) the slopesf(c+h)鈭�f(c)handf鈥�(c)

Short Answer

Expert verified

(a)

(b) h=1 and f(c+h)-f(c)=0.5

(c) Slopes is 0.5 and f'(c)=0.5

Step by step solution

01

Part (a) Step 1. Given information.

For the graph of f appearing next at the left, label each of the following quantities to illustrate that

f鈥�(c)鈮�f(c+h)鈭�f(c)h

02

Part (a) Step 2. Locate c,c+h,f(c),f(c+h)

After locating the point, the graph is :

03

Part (b) Step 1. Find the distance h and f(c+h)-f(c)

By looking at the graph, we can said that the values of h is 1 unit in the graph andf(c+h)鈭�f(c)is 0.5

04

Part (c) Step 1. Find the slope and f'(c)

We have f(c+h)鈭�f(c)=0.5and h=1, therefore the slopes is:

f(c+h)鈭�f(c)h=0.51=0.5

Again,

f鈥�(c)=limh鈫�0鈥�f(c+h)鈭�f(c)h=limh鈫�0鈥�0.51=0.5

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