maths is a headache esp when u get qns like e one below:
Maisie the Wonder Dog has a very good nose for the neighbours' BBQ. When Lisa is cooking steaks on the BBQ, the wonderful aroma has a concentration as a function of position given by the formula
i guarantee u tat when u see e formula u confirm will get high
C(x,y) = e^< -0.02(x-10)^2 - 0.01(y-5)^2 >
woohoo... e eqn is so violent.
(a) Find the directinal derivative of C in the direction of the vector 10i + 5j at (0,0).
(b) Maisie is at position (0,0). If she starts to walk directly toward the position (10,5), what is the instataneous rate of change of the concentration of the aroma?
(c) Find the magnitude and direction of the maximum directional derivative of C at (0,0).
(d) In what direction should Maisie move from (0,0) in order to maximize the rate at which the concentration of the aroma is increasing?
