Given f(2) = 2, f′(2) = 1, g(2) = 3 and g′(2) = 4

Question

If F(x) = f(x)g(x) then F′(2) = ?

If F(x) = f(x)/g(x) then F′(2) = ?

Answer 1

f(2) = 2, f′(2) = 1, g(2) = 3 and g′(2) = 4

F(x) = f(x)*g(x)

Using the product rule

F'(x) = f'(x)*g(x) + f(x)*g'(x)

F'(2) = f'(2)*g(2) + f(2)*g'(2)

F'(2) = 1*3 + 2*4 = 3+8

= 11

F(x) = f(x)/g(x)

Using the quotient rule

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

F'(2) = [f'(2)*g(2)-f(2)*g'(2)]/g(2)²

F'(2) = [1*3-2*4]/3²

= -11/9