Find the unit vectors in the directions of steepest descent

Assignment Help Mathematics

Reference no: EM131006086

Consider an elliptic paraboloid

f (x, y) = 4 - x² - y²/4.

a. Find the xy-, yz- and xz-traces of the graph of f(x, y) and sketch the graph.

b. Write down the equation of the level curve which passes through a point (2.4). Sketch the level curve.

c. Find the unit vectors in the directions of the steepest descent and the steepest ascent at (2, 4). Mark these directions on the graph in (b).

d. Verify that the gradient at (2, 4) is orthogonal to the level curve through this point.

(e) Write down the equation of the tangent line to the level curve at (2, 4).

Reference no: EM131006086

Questions Cloud

Construction and working of fabry perot interferometer : Construction and working of Fabry perot interferometer

What are the requirements to prove an extortion case : Expain 4 different times- What are the requirements to prove an extortion case

Assume that an economy is characterized by the equations : Assume that an economy is characterized by the following equations: C = 100 + (2/3)(Y − T ) T = 600 G = 500. Write the numerical IS curve for the economy, expressing Y as a numerical function of G,T, and r.

Point income elasticity of demand : 1. Estimate an empirical demand function for one-month memberships using the data gathered from the firm's 24 clubs. (Assume the demand function is linear. Further assume that the only variables likely to significantly affect the demand for one-mo..

Find the unit vectors in the directions of steepest descent : Find the unit vectors in the directions of the steepest descent and the steepest ascent at (2, 4). Mark these directions on the graph in (b). Verify that the gradient at (2, 4) is orthogonal to the level curve through this point.

Find parametric equations of the straight line : Find parametric equations of the straight line that passes through the point A (1, 5, -3) and is orthogonal to the plane 2x + y - 3 z = 2 and At what point does this line intersect the plane?

Home versus foreign countries while they remain in autarky : What is the difference between relative factor endowments and relative factor intensities? What does the Hecksher-Ohlin theorem say about home versus foreign countries while they remain in autarky? What happened to the Leontief paradox when human ca..

What are executory costs : What are executory costs? How are they accounted for by the lessee in a capital lease when paid by the lessee? When paid by the lessor? Explain.

Case brief - roberts vs century contractors inc : CASE BRIEF ASSAIGNMENT. Case - Roberts v. Century Contractors, Inc. 592 S.E.2d 215

User Account

All Pages