Oh okay:)! So then it wouldn't be parallel to the gradient vector because f'(pi) = <2pi, -1> which is not a multiple of the gradient i calculated. So, the particle isn't traveling in the direction of greatest temperature increase.
Thanks so much!
Homework Statement
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...
Okay, so then that would mean that t would have to be any real number that satisfies any multiple of <4,0,2> .. which would only be when t is 1, since we have a constant 1 in the acceleration formula. Am i on the right track?
Thanks so much!:)
Homework Statement
A particle travels along a path C in R^3 which velocity v(t) =<t^2, cos(pi*t), t> at time t. Assume that the particle's initial position is at the point p=(1, 0, -1). Find all times t at which the particle is accelerating in a direction that is perpendicular to the plane...