1. Let y=AeBx. (a) Calculate the forward Legendre transform of y(x) to obtain g(p) where g=ypx and p=dxdy (b) Calculate the reverse Legendre transform of your solution to part (a) and verify that you obtain the original expression y(x). The reverse Legendre transform is defined by y=px+g where x=dpdg. (c) For A=2 and B=0.5, generate a plot of y(x) and a family of tangent lines in accordance with the result found in part (a). Check that the tangent lines go through the expected points as x=0,1 and 2 . 1. Let y=AeBx. (a) Calculate the forward Legendre transform of y(x) to obtain g(p) where g=ypx and p=dxdy (b) Calculate the reverse Legendre transform of your solution to part (a) and verify that you obtain the original expression y(x). The reverse Legendre transform is defined by y=px+g where x=dpdg. (c) For A=2 and B=0.5, generate a plot of y(x) and a family of tangent lines in accordance with the result found in part (a). Check that the tangent lines go through the expected points as x=0,1 and 2