A metal plate is heated so that its temperature at a point (x, y) is T(x, y) = x²e-2x*+3y). A bug is placed at the point (1, 1). The bug heads toward the point (2, –4). What is the rate of change of temperature in this direction? (Express numbers in exact form. Use symbolic notation and fractions where needed.) per unit length Consider the direction the bug should head to warm up at the fastest rate. Find the rate of change of temperature in this direction. (Express numbers in exact form. Use symbolic notation and fractions where needed.) per unit length Consider the direction the bug should head to cool off at the fastest rate. Find the rate of change of temperature in this direction. (Express numbers in exact form. Use symbolic notation and fractions where needed.) per unit length

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