Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given by x (0) find the the functions #1 (t) and x2(t). Enter your answer as a 2x1 column vector, i.e x2 (t).

Suppose that the position function of a particle moving on a coordinate line is given by s(t) 1³-2t² + 3t -7 in meters, where t is in seconds. (a) Find the velocity and acceleration functions; (b) Analyze the direction of the motion that shows when the particle is stopped, when it is moving forward and/or backward; (c) Analyze the change of speed that shows when it is speeding up and/or slowing down; (d) Find the total distance traveled by the particle from time t =0 to t = 6 seconds.

What is the velocity​ vector?

18 > (a) Find the direction for which the directional derivative of the function f (x, y) = 7xy² + 5x² is a maximum at P = (-1,2). (Use symbolic notation and fractions where needed. Give your answer in vector form.) direction: (b) Find the maximum value of the directional derivative. (Use symbolic notation and fractions where needed.) ||Vf(-1,2) || =