Consider g(x, y) = xye". (a) Find Vg(1,0). (b) What is the equation of the tangent plane to g(x, y) at (1,0)? (c) Find the direction derivative of g(x, y) at (1,0) in the direction of v = 2i - j.

8) A runner was training for a 21 mile long race. The distance D (in miles) in function of time t (in weeks) is given by: D = 2(t-1)² +15 a) b) c) How many miles have done the runner in the first week? What is the average rate of training between the first and the third week? dD Calculate the derivative of D with respect to time dt and explain the obtained answer.

Consider the curve x3 + y2 - 4xy = -2