If h(x)=f(x)/g(x), calculate h′(3) given that

Question

f(3)=3, f'(3)=-1

g(3)=-1, g'(3)=4

Answer 1

h(x)= f(x)/g(x)

g(3) = 1, f(3) = 3

h(3) = f(3)/g(3) = 3/-1 = -3

f'(3)=-1, g'(3) = 4

quotient rule for derivatives:

derivative = denomnator times derivative of numerator minus numerator times derivative of denominator

all divided by the denominator squared:

for h(x) = f(x)/g(x)

h'(x) = [g(x)f'(x) - f(x)g'(x)]/(g(x))^2

h'(3) =[-1 - (3)(4)]/1^2 = -1-12 = -13

h'(3) = -13