if g(x)=max|y^2-xy| (0≤y≤1) then the minimum value of g(x) for real x

2 years ago

Share

Answers : (3)

                    

Hi Debdutta,


 


As y is always positive, let us see what happens in these cases


 


1. x>0, in this case we are subtracting a positive term from y^2 and hence possibility of minimum


2. x<0, in this case we are subtracting a negative term from y^2 and hence a possibility for maximum.


 


So we say g(x) = max|y^2 - xy|, x>0 for g(x) = minimum.


 


Now say y lies in (0,1] ie y is not equal to zero. In this case there will always exist a positive x where g(x) is always > 0.


And hence the minimum value will be possibile for x=y, ie the minimum value will be 0.


In case y=0, then g(x) = 0 for all x, and in this case also minimum value is 0.


 


Hence minimum value of g(x) is clearly 0.


 


Hope it helps.


 


Regards,


Ashwin (IIT Madras).

2 years ago
                    

sorry mr ashwin by mistake i approved ur ans but the ans is 3-8^1/2 i think u r not considering the word max before mod

2 years ago
                    

Hi Debdutta,


 


3-√8 is definitely not the right answer. You could have checked that on your own.


 


I have considered the word MAX in the question.


 


Clearly 0 is lesser than 3-√8, as 3-√8 is a positive number.


So minimum value has to be 0.


If somewhere you have seen the answer to this question as 3-√8, then it is wrong.


(Or else you have not mentioned some condition in the question)


Thanks.


 


Regards,


Ashwin (IIT Madras).

2 years ago

Post Your Answer

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
Domain Image is attached
 
 
Ans: 1st Part: Explaination: when [-1, 1] lie in the interval [-pi/2, pi/2]. 2nd Part: Suppose for ths ‘x’ in the base Suppose for ths ‘x’ in the base Final Solution:...
  img
Jitender Singh 22 days ago
Image is attached . How to draw graph of this function?
 
 
Ans: Domain is given as R. function passes through origin. So, function is always increasing . From here, find the region where f’’(x) is +ve & -ve. -> Concave Up ->...
  img
Jitender Singh 16 days ago
Differential of log^n x
 
 
Ans: It is a zero by zero form, so apply L’Hospital rule Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty
  img
Jitender Singh 16 days ago
A certain polynomial P(x),x E R WHEN DIVIDED BY (x-a),(x-b) and (x-c) leaves remainder a,b,c.then find the remainder when P(x) is divided by (x-a)(x-b)(x-c) where a,b,c are distinct
 
 
it is clear that f(a) is the remainder when f(x) is divided by x-a and when f(x) is divided by q(x) the remainder will be having degree less than q(x) so when P(x) is divided by...
  img
MuraliKrishna Medavaram 5 months ago
 
Thanks and Regards, M.MURALIKRISHNA askIITians faculty
  img
MuraliKrishna Medavaram 5 months ago
 
The polynomial P(x) - x has roots a,b, and c Hence P(x) - x = (x-a)(x-b)(x-c) Q(x) for some polynomial Q(x) or P(x) = Q(x) (x-a)(x-b)(x-c) + x It immediately follows that the remainder when...
 
mycroft holmes 5 months ago
every vectors has magnitude???
 
 
Yups. every vector has magnitude either 0 or any number
 
Darpan Kochar one year ago
 
yes even null vector O has null magnitude
 
chandan jha one year ago
prove that four straight lines represented by the equation 12x 2 +7xy -12y 2 =0 and 12x 2 +7xy -12y 2 -x +7y -10 form a square
 
 
Hello Student, 12x2+7xy -12y2=0 12x2+7xy -12y2-x +7y -10 with first x=(-7y +- yroot(49+144*4))/24 you will get 2 lines from here with second do the same thing x=(-7y+1 +- root((7y-1)^2...
  img
Arun Kumar one month ago
View all Questions »