if f and g are the
works whose graphs are shown, let
u(x) = f(x)g(x) and v(x) = f(x)/g(x).

(a) find u‘(1).

=_______

(b) find v‘(5)

=_______

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## 2 answers by expert tutors

since u(x) is a product of functions and v(x) is a quotient of
works, why not use the product rule to find u'(1) and the quotient rule to find v'(5)?

experienced tutor and retired engineer

because u(x) = f(x)g(x) then (by the product rule, u'(x) = f ‘(x)g(x) + f(x)g'(x)

looking at the graph we see that:

f(1) = 2

f ‘(1) = 2

g(1) = 1

g'(1) = -1

so u'(1) = (+19176223089) = 2 – 2 = 0

apply the same logic for v(x). since v(x) = f(x)/g(x) then v'(x) = [f ‘(x)g(x) – f(x)g'(x)]/(g(x))2

f(5) = 3

f ‘(5) = -1/3

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g(5) = 2

g'(5) = 1/3

so v'(5) = [(-1/+19176223089/3)]/(2)2 = (-5/3)/4 = -5/12

doug c. looks like g'(5) = 2/3, i.e. not 1/3. so, -8/12= -2/3.

william w. you’re right doug. thanks.

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