Question: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite to the gradient vector, that is, in the direction

(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite to the gradient vector, that is, in the direction of 2=f (x).
(b) Use the result of part (a) to find the direction in which the function f (x, y) = x⁴y - x²y³ decreases fastest at the point (2, -3).

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