1. The problem statement, all variables and given/known data A particle travels across a heated plate according to the path f(t) = (t^2, sint) at the time t seconds. The temperature T(x,y) at position (x,y) on the plate is given by T(x,y)= 200E^[-(x^2 + y^2)] degrees Celsius. At time t=pi seconds, is the particle traveling in the direction of greatest increase in temperature on the plate from position (pi^2, 0)? Explain why or why not. 2. Relevant equations 3. The attempt at a solution I have that at time t=pi the particle's rate of change in temperature is -800(pi^3)e^[-(pi^2+1)] - 400e^[-(pi^2+1)] or -0.479498546 Also, I found the the gradient of T is the direction of the maximal rate of increase so i found that the gradient of T(pi^2,0) = <-400pi*e^(-pi^2), 0> But now i dont know what to do.