(a) If
(b) Find the second directional derivative of
Want to see the full answer?
Check out a sample textbook solutionChapter 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_forwardCalculate the directional derivative of the vector field f(x,y,z) = (yz)i - (x)j -(y)k at the point A (-1,-1,1) in the direction of the normal outside the level surface x² + z² = 1 - 4y at the point B (1,-1, 2).arrow_forwardFind the gradient vector field of f. f(x, y, z) = 7 x2 + y2 + z2arrow_forward
- Suppose that in a certain region of space the electric potential V is given by the function V (x, y, z) = 5x2 −3xy + xyza) Determine the rate of change of the potential at P = (3,4,5) in the direction of the vector v = (1, −1, 1).b) In what direction does V change faster in P?c) What is the maximum rate of change of V in P?arrow_forwardFind the gradient fields of g(x, y, z) = xy + yz + xzarrow_forwardDetermine the directional derivative of the function f (x, y, z) = x2 + xy + y + z2 in point P = (1; 2; 1) and in the direction of a vector orthogonal to the surface 2x2 - 3y2 - z + 1 = 0 in the point A = (2,1,6)arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning