Answer
$$\left( {\frac{1}{3},e} \right)$$
Work Step by Step
$$\eqalign{
& y = {e^{3x}} \cr
& {\text{Calculate the derivative}} \cr
& \frac{{dy}}{{dx}} = 3{e^{3x}} \cr
& m = 3{e^{3x}} \cr
& {\text{The derivative passes through the origen, then we have the}} \cr
& {\text{point }}\left( {0,0} \right),{\text{ the equation is given by}} \cr
& y - {y_1} = m\left( {x - {x_1}} \right) \cr
& {e^{3x}} - 0 = 3{e^{3x}}\left( {x - 0} \right) \cr
& {\text{Solve for }}x \cr
& {e^{3x}} = 3x{e^{3x}} \cr
& {e^{3x}} - 3x{e^{3x}} = 0 \cr
& \left( {1 - 3x} \right){e^{3x}} = 0 \cr
& 1 - 3x = 0,{\text{ or }}{e^{3x}} = 0 \cr
& 1 - 3x = 0 \cr
& x = \frac{1}{3} \cr
& {\text{The point is }}\left( {\frac{1}{3},f\left( {\frac{1}{3}} \right)} \right) \cr
& f\left( {\frac{1}{3}} \right) = {e^{3\left( {\frac{1}{3}} \right)}} = e \cr
& {\text{The point is }}\left( {\frac{1}{3},e} \right) \cr} $$
