The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
0 votes
431 views
  1. In questions 1.1 to 1.7 below, one or more of the alternatives are correct.  Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book.  Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up.

1.7 The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has

  1. no local extremum
  2. one local minimum but no local maximum
  3. one local maximum but no local minimum
  4. one local minimum and one local maximum
asked in Calculus by Veteran (59.6k points)
retagged by | 431 views

1 Answer

+6 votes
Best answer

Answer: A

r = $\frac{\partial^2 f}{\partial x^2}$ = 2y

s = $\frac{\partial^2 f}{\partial x \partial y}$ = 2x - 3

t = $\frac{\partial^2 f}{\partial y^2}$ = 0

Since, rt - s2 <= 0, (if < 0 then we have no maxima or minima, if = 0 then we can't say anything).

Maxima will exist when rt - s2 > 0 and r < 0.

Minima will exist when rt - s2 > 0 and r > 0.

Since, rt - s2 is never > 0 so we have no local extremum.

answered by Boss (34k points)
selected by
0

When x = 1.5, s2 = 0 and 0 - 0 = 0. 

0
Corrected.


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

41,071 questions
47,669 answers
147,407 comments
62,387 users