Question

In: Math

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).

Solutions

Expert Solution

u(x) = f(x) g(x)

u'(x) = f'(x) g(x) + f(x) g'(x)

u'(1) = f'(1) g(1) + f(1) g'(1) = 2 * 1 + 2 * (-1) = 2 - 2 = 0

v(x) = f(x) / g(x)

v'(x) = ( g(x) f'(x) - f(x) g'(x) ) / g^2 (x)

v'(5) = ( g(5) f'(5) - f(5) g'(5) ) / g^2 (5) = ( 2*(-1/3) - 3*(2/3) ) / 2^2 = (-8/3) / 4 = -2/3

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