Question
Asked Sep 27, 2019
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The graphs of the function f (given in blue) and g(given in red) are plotted above. Suppose that u(x) = f(x)g(x) and v(x)=f(x)/g(x). Find each of the following:

u′(1) = ?

v′(1) = ?

-1
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-1

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Expert Answer

Step 1

From the given graph it can clearly observed that f (1) = 1 and g (1) = 3.

Given that u (x) = f (x) g (x), then

(x)f(x)g (x) g(x)f'(x) [Product rule
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(x)f(x)g (x) g(x)f'(x) [Product rule

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Step 2

f'(1)- )(0)
1 0
1 -0
1-0
=1
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f'(1)- )(0) 1 0 1 -0 1-0 =1

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Step 3

...
g(1) (1)-g(0)
1 -0
3-4
1-0
=-1
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g(1) (1)-g(0) 1 -0 3-4 1-0 =-1

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Tagged in

Math

Calculus

Derivative