The following equation, y(x)=10x2 a) Find the Legendre transformation of this parabola, =(P), where P=dxdy (b) Draw (consider a range from x15 to x15 and from y25 to y25 ) straight lines with slopes P=0,0.5,1,2,3 and with intercepts satisfying (P) found in the part and (a). (Drawing each line is made easier by calculating the intercepts on the x-axis and the y-axis. Be y(x)=AeBx (a) Find the Legendre transformation (P) of y(x) (b) Evaluate the inverse Legendre transformation of (P) and prove that the result is y(x)