Show that the gradient of a differentiable function f points in the direction of greatest increase.

Question:

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:50 AM

See More Questions

Show that the gradient of a differentiable functional on n comprises the vector of its partial derivatives, that is, Vf(x) = (Dfx), Dfx)...., D fx)
A differentiable function f : I R is said to be uniformly differentiable on I := (a, b) if for every Îµ > 0 there exists Î´ > 0 such that if 0 Show that if f is uniformly...
A differentiable function f on a convex, open set S in n is convex if and only if for every x0; x S. f is strictly convex if and only if for every x x0 S. (32)
General Ledger Accounts Account: Cash Date Description Opening Balance Account: Date Petty Cash Description Opening Balance Account: Date Accounts Receivable Description Opening Balance Account: Date...
Compute a one-way ANOVA on the following data. Determine the observed F value. Compare the observed F value with the critical table F value and decide whether to reject the null hypothesis. Use (...
The Georgia Ceramic Company has an automatic glaze sprayer that has been used for the past 10 years. The sprayer can be used for another 10 years and will have a zero salvage value at that time. The...
Do you think it is possible to have win-win negotiations? Why or why not?
Required Identify which of the following items are added to or subtracted from the unadjusted bank balance to arrive at the true cash balance. Distinguish the additions from the subtractions by...
How do ethical leaders demonstrate authenticity and ethical authenticity, aligning personal values with organizational goals, and modeling ethical behavior to cultivate ethical awareness and...
The following information is available for two different types of businesses for the 2016 accounting year. Hopkins CPAs is a service business that provides accounting services to small businesses....
If a differentiable functional f is increasing, then f(x) 0 for every x X; that is, every partial derivative Dxi f[x] is nonnegative.
f: X m, X n is differentiable x0 if and only if each component fj is differentiable at x0. The matrix representing the derivative, the Jacobian, comprises the partial derivatives of the components...
Assume the same facts as in Problem 33, except that Kyras business pays $60,000 of W2 wages and generates $200,000 of qualified business income. Kyra also has a part-time job earning wages of $11,200...
Decompose the $(i+1)$ th block pulse function component using two delayed unit step functions, and graphically prove that the integration of these component functions finally result in the figure...
An account planner is often considered the consumer advocate. Pick a brand that you like and usea brand that would be your best friend. What three things does the consumer like most about the brand?...
Derive the relation $\boldsymbol{\Phi}=\mathbf{W} \Psi$ where $\mathbf{W}$ is the Walsh matrix, $\boldsymbol{\Phi}$ is the Walsh function vector, $\Psi$ is the block pulse function vector of...
Explain why the operational matrix for integration $\mathbf{P}$, is of an upper triangular form. What are the mathematical advantages of an upper triangular matrix?
What is e-commerce.
The regression equation is computed for a set of n = 18 pairs of X and Y values with a correlation of r = +0.50 and SS Y = 48. a. Find the standard error of estimate for the regression equation. b....
If the joint cost function for two products is C(x, y) = xy2 + 1 dollars (a) Find the marginal cost (function) with respect to x. (b) Find the marginal cost with respect to y.
Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per...
The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day. (a) Express the cost as a function of the number of...
At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in2. Below the surface, the water pressure increases by 4.34 lb/in2 for every 10 ft of descent....
What is Data Flow Diagram? Explain the Steps ti draw data flow diagram?
What is the purpose of data flow diagrams? Do data flow diagrams show system logic and decision points? Explain.
Online Shopping of clothes. Please solve the following part: Logical Model Design .. 1.0 Data Flow Diagram.. 1.1 Context Diagram.. 1.2 Level 0 Data Flow Diagram.. 1.3 Level 1 Data Flow Diagram.. 1.4...

Show that the gradient of a differentiable function f points in the direction of greatest increase.

Question:

Step by Step Answer:

The directional derivative Measures the rate of incr...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions