Waste less time on Facebook — follow Brilliant.
×

Maximise the Absolute

Let \(m\) and \(n\) be distinct positive integers.

Find the maximum value of \(|x^m - x^n|\), where \(x\) is a real number in the interval \((0, 1)\).

Note by Sharky Kesa
2 years, 11 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Note that \(x^r\) is a strictly decreasing function when \(x\in(0,1)\), and the maximum value would be achieved when \(m\) is the least and \(n\) is the most, in this case, \(m=1\) and \(n\to\infty\), where \(|x^m-x^n|=|x^1-0|=x\).

Note: @Sparsh Goyal posted the numerical answer first. Kenny Lau · 2 years, 4 months ago

Log in to reply

The answer should be "x" ! Sparsh Goyal · 2 years, 5 months ago

Log in to reply

In terms of m and n? Kenny Lau · 2 years, 5 months ago

Log in to reply

whats the answer Manish Bhargao · 2 years, 5 months ago

Log in to reply

0 Asama Zaldy Jr. · 2 years, 5 months ago

Log in to reply

@Asama Zaldy Jr. I dont think it will have a numeric value as answer as "x" is variable and there are infinite nos. between 0 and 1... Sparsh Goyal · 2 years, 5 months ago

Log in to reply

@Sparsh Goyal Note that it asks for a maximum value. Sharky Kesa · 2 years, 5 months ago

Log in to reply

Simplest thing I can think of \(|1^1-0^1|\).... It has to be more complicated than this... Trevor Arashiro · 2 years, 5 months ago

Log in to reply

@Trevor Arashiro He put (0,1), which means 0 & 1 not included, so it must be something else!! Vivek Bhagat · 2 years, 5 months ago

Log in to reply

@Trevor Arashiro That doesn't work at all. I think you typoed. Sharky Kesa · 2 years, 5 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...