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

Simon G.

asked • 11d# If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x).

If *f* and *g* are the functions 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)

=_______

## 2 Answers By Expert Tutors

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) = (2)(1) + (2)(-1) = 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

g(5) = 2

g'(5) = 1/3

So v'(5) = [(-1/3)(2) - (3)(1/3)]/(2)^{2} = (-5/3)/4 = -5/12

William W.

10d

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Doug C.

Looks like g'(5) = 2/3, i.e. not 1/3. So, -8/12= -2/3.11d