Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 400 off


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

4 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).

4 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

4 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).

4 years ago

Post Your Answer

Other Related Questions on Differential Calculus

How to determine principal period of f(x-1)+f(x+1)=3^1/2f(x)
Bhai, HashLearn is providing unlimited doubt clearing with IIT tutors for a month at Rs. 199. You should try them. Better than waiting here for a response
Ankit 16 days ago
What answer for this sum in differentiate with respect to x
Substitute x= tan(z) in the question then after using identity of cos(2z) u will get the given function as 2∆ I.e. 2*arctan(x) and its differentiation is 2/(1+ x^2)...hope it helps
rishabh 20 days ago
What answer for this sum in differentiate with respect to x ?????? In complete question.... because you write sum, what is mean of sum.
Kumar one month ago
find the maximum and minimum value of g(x) = x^3 + 1 plz reply as fast as you can
the given function is g(x)=x^3+1 for determining maximum and minimum values we have to find out that the given function is increasing or decreasing so differentiate the given function on...
SREEKANTH 4 months ago
g(x) = x^3 + 1 differentiate it g’(x) = 3x^2 = 0 hence slope is always positive. the graph will approach to + infinity and – infinity as x increases and decreases. Therfoore maximum and...
Vikas TU 4 months ago
Solve this Let a = i + 2 j + 3k and b = 3 i + j find the unit vector in the direction of a+b?
Given a = i + 2 j + 3k and b = 3i + j a + b = i + 2 j + 3k + 3i + j = 4 i + 3 j + 3k ∴ The unit vector in the direction of =± 4 i + 3 j + 3k 16 + 9 + 9 =± a+b |a+b| 4 i + 3 j + 3k | 4 i + 3 ...
KUNCHAM SAMPATH 10 months ago
how to integrate this ? please give me solution to this queston. thanks
We can use integration by partial fraction here
Nishant Vora one month ago
The sol. set of inequility (3 x -4 x ).ln(x+2) /x 2 -3x-4 is?
Inequality is missing in this question. Only expression is provided. PLease provide the complete question.
Harsh Patodia one month ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 400 off

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