The mass density function of a substance is given by: p(x, y) = (x + y) e-. A particle is moving along the hyperbola z-y=1 with the parametric function (t) = (cosh(t), sinh(t)) for 1 (-1,1) a) Determine the time when the density of the particle is maximized. b) Find the tangent vector to the path of the particle at the time t determined in part (a). c) Calculate the rate of change of the density of the particle at the time t obtained in part (a).