Chapter 14.6, Problem 27E

(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 $-\nabla f\left(x\right)$.

(b) Use the result of part (a) to find the direction in which the function $f\left(x,y\right)=x^{4}y-x^2{y}^3$ decreases fastest at the point $\left(2,-3\right)$.