Total Price: R

There are no items in this cart.
Continue Shopping


“Hurray! You have won the gift voucher. Redeem your points now."



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

3 years ago


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.



Ashwin (IIT Madras).

3 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

3 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)




Ashwin (IIT Madras).

3 years ago

Post Your Answer

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
limit x tends to 0 e^(-x 2 /2) – cosx = ? x 3 sinx
answer is 1/12 best method for these type of questions is series expansion when we use series of e x , sinx , cosx , value of limit will be coefficient of x 4 , as x is tending to 0 and all ...
ng29 2 months ago
you can solve the given question by using lhospital very useful and time saving rather series expansion 0/0 form is obtained diffrentiate until you are out of the form finally put x=0 the...
grenade 2 months ago
Dear student, Please post the correct question. Thanks Nishant Vora
Nishant Vora 3 months ago
where is the question kindly post it again to get it be answered
ng29 3 months ago
Hi Friends, Do you all know that askiitians has launched self study courses at negligible price along with discount of 30% so that we students can get help in our studies. These lectures...
These self-study packages are actually free to the enrolled students!! The test papers and video solutions given are brilliant and super helpful :D
Kalyani Jayachandran Menon 11 days ago
the equation sin^4x+cos^4xforall real values of x
HInt. Simplify the given equation using formula (a 2 + b 2 ) = (a+b) 2 – 2ab. Thanks.
Vijay Mukti 9 days ago
plz post ur complete question
noogler 9 days ago
Consider an A.P. with first term 'a' and the common difference 'd'. Let Sk denote the sum of its first K terms. If x kx S S is independent of x, then (A) a = d/2 (B) a = d (C) a = 2d (D)...
Hello Student, can you please specify the condition in the question properly becoz its not clear Thank you...
Nishant Vora 10 months ago
Hello student, Now this will be independent of ‘x‘ only when 2a=d Option (A)
Nishant Vora 10 months ago
okay here the question again...Q.Consider an A.P. with first term 'a' and the common difference 'd'. Let Sk denote the sum of its first Kterms. If Skx/Sx is independent of x then which one...
Henry Kashyap 10 months ago
A rop of length l slides with it’s ends on co-ordinates axis. Find the locus of it’s midpoint.
see, if (a,b)are the x n y axes,a 2 +b 2 =l 2 .....(c,d) midpt....c=a/2,,d=a/2....c^2+d^2=l^2/4....x^2+y^2=l 2 /4
RITABRATA SANYAL 11 months ago
View all Questions »