Question
Asked Sep 30, 2019
Let G 6f- g, where the graphs of f and g are shown in the figure to the right. Find the following
derivative.
Ay
8-
G'(5)
y = f(x)
4-
X
0fygk)
4
G'(5)
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Let G 6f- g, where the graphs of f and g are shown in the figure to the right. Find the following derivative. Ay 8- G'(5) y = f(x) 4- X 0fygk) 4 G'(5)

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Expert Answer

Step 1

The given graph has two functions f(x) and g(x). We consider the interval from 4<x<8, Calculate the slopes for both the graphs by writing equation of a line using two point form and carry out the mathematical operations as asked in the question.

G 6f-g
G' 6f-g
Given;
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G 6f-g G' 6f-g Given;

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Step 2

Consider two points on the blue graph (x1,y1)=(4,1) and (x2,y2)=(7,7).Using two-point form, the equation is written as,

y-y
— х,
У -У.
у-1
х—4
4 7
1 7
y-1
х—4
-6
3
Simplifying
у -1%32(х- 4)
y= 2x 7
Comparing with y mx+c,we get m
f(x) 2
1
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y-y — х, У -У. у-1 х—4 4 7 1 7 y-1 х—4 -6 3 Simplifying у -1%32(х- 4) y= 2x 7 Comparing with y mx+c,we get m f(x) 2 1

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Step 3

r two points on the red graph g(x); (x1,y1)=(4,5) and (x2,y2)=(8,1).Using tw...

х —4
y-5
4 8
5-1
x- 4
4
-4
Simplifying
у -5%3-1(х-4)
y=-x+9
Comparing with y = mx+c,we get m
g'(x) (1)
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х —4 y-5 4 8 5-1 x- 4 4 -4 Simplifying у -5%3-1(х-4) y=-x+9 Comparing with y = mx+c,we get m g'(x) (1)

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Tagged in

Math

Calculus