x f(x) f ′(x) g(x) g′(x)
3 4 1 6 1
4 −2 −6 1 3
5 1 3 4 3
6 5 1 3 −2
The functions f and g have continuous derivatives. The table gives values of f, f ′, g, and g′ at selected values of x.
Part A: Find h′(3) if h(x) = g(f(x)). (5 points)
Part B: Find m′(2) if m(x) = f(x2). (5 points)
Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 6. (10 points)
Part D: Let j of x is equal to g of x divided by f of x. Find j′(4). (10 points)
