(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite to the gradient
(b) Use the result of part (a) to find the direction in which the function
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Chapter 14 Solutions
Calculus (MindTap Course List)
- Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.arrow_forwardFind the gradient of the function z = cos(x2 + y2), at the given point (3, −4)arrow_forwardThe gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) isarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning