
The point P(x, y) that minimize the sum of distances between the fixed points lying in a plane.
(a)
To Show:
That the condition is equivalent to .
(b)
To Show:
That the function is differentiable except at points A, B and C and the minimum of occurs either at P satisfying the equation , where e, f and g are the unit
(c)
To Prove:
That the equation , where e, f and g are the unit vectors in the direction of vectors holds if and only if P is the Fermat point, defined as the point P for which the angles between the segments and are all 120°.
(d)
To Show:
That the Fermat point does not exist if one of the angles in is greater than 120° and the point which exist in this case is different from Fermat point.

Want to see the full answer?
Check out a sample textbook solution
Chapter 14 Solutions
Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover
- i don't understand how to get these answers please help!arrow_forwardEnter your answer in interval notation. No decimal entries allowed. Type oo (lower case o) for ∞ and -oo for -∞ if needed. Domain: Question Help: Message instructorarrow_forwardWrite a formula for the function g that results when the graph of the function f(x) = = 4 X is reflected about the y-axis, horizontally compressed by a factor of 2, shifted 7 units left, reflected about the x-axis and shifted 3 units up. g(x): = Question Help: Message instructorarrow_forward
- Question 7 4 pts 1 Details The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $10.4 billion?arrow_forwardQuestion 7 4 pts 1 Detai The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e 0.3387x, where x = 0 corresponds to 1998. In what year did/will the exports reach $10.4 billion?arrow_forwardWrite a formula for the function g that results when the graph of the function f(x) = = 4 X is reflected about the y-axis, horizontally compressed by a factor of 2, shifted 7 units left, reflected about the x-axis and shifted 3 units up. g(x) = Question Help: Message instructorarrow_forward
- Question 3 Use the graph of f to evaluate the following: 3 pts 1 D 6 f(x) 5 4 3 2 1 -1 1 2 3 4 5 เค -1 x The average rate of change of f from 1 to 4 =arrow_forwardB Find the domain the function graphed below. Express in interval notation 5 3 pts 1 De 3 2 1 -5 -4 -3 2 -1 2 3 4 5 -2 -3 -4 5 Domain:arrow_forwardFind the domain the function graphed below. Express in interval notation 3 2 -5 4-3 12 -1 1 2 3 4 2 -3- 4 5+ Domain: Question Help: Message instructor Question 3arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





