Question

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x) = the quotient of f of x and g of x..

Answer 1

just have to keep track of all the values they have, and what x value you are using...

Answer 2

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

h'(x) uses the quotient rule to get

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

Answer 3

they want h'(x), when x=1

h ' (1) = [ g(1) * f '(1) - f(1) * g'(1)] / g(1)^2

put all those values in

Answer 4

[ 3*(-4) - 4*(-3)] / 3^2

looks like 0