Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let f : rn ? r be a differentiable function. suppo

Let f : Rn ? R be a differentiable function. Suppose that a point x? is...

90.2K

Verified Solution

Question

Advance Math

Let f : Rn ? R be a differentiable function. Suppose that apoint x? is a local minimum of f along every line passes throughx?; that is, the function

g(?) = f(x^? + ?d)

is minimized at ? = 0 for all d ? R^n.

(i) Show that ?f(x?) = 0.

(ii) Show by example that x^? neen not be a local minimum of f.Hint: Consider the function of two variables

f(y, z) = (z ? py^2)(z ? qy^2),

where 0 < p < q.

Answer & Explanation Solved by verified expert
3.8 Ratings (377 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Basic Math
1.2K views

Make a simulation to verify the following theorem: if X1 ? N(µ1, (? 1)^2 ), X2...

Finance
1.2K views

Company HDE is expected to pay an interim dividend of $1.00 three months from now and...

Physics
1.2K views

Hot & Cold compress 1. What are compresses? 2. What conditions would benefit from hot compresses? 3. What...

Biology
1.2K views

A scientist is researching the cell division and differentiation for neurons, or nerve cells. The...

Physics
1.2K views

1 How far from above the center point of the screen will the first mimimum...

Geometry
1.2K views

4 A baseball player invested 2 million of a bonus received in an account that...

Basic Math
1.2K views

Suppose a closed economy generates 2000 output and income in equilibrium Suppose also that the...

Basic Math
1.2K views

A 2 drum lottery has 48 white balls in the first drum and 36 red...

Accounting
1.2K views

Tamarisk Firm is considering whether to outsource the manufacture of subcomponent JXY. The accounting department...

Accounting
1.2K views

Depreciation Method Problem 6.13 Comprehensive Depreciation Calculations *** Kamadhenu Dairy has four assets, data on...

Accounting
1.2K views

How often should a company perform a physical inventory count? Are companies required to perform...

Accounting
1.2K views

Budgetary performance for cost center Cumming Company's costs were under budget by $29,000. The...