Waste less time on Facebook — follow Brilliant.
×

In Problem with a problem

This is a bit confusing for me.

Note by Kushal Patankar
2 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Try to realize that \( f(x) = x^2 - 2|x| \). Try using the graph. If you still don't get, reply I'll add a detailed solution. Just to check are the answers C, D , D ?

Sudeep Salgia - 2 years, 4 months ago

Log in to reply

I am unable to graph \(g(x)\).

Kushal Patankar - 2 years, 4 months ago

Log in to reply

img

img

Here is the image for the graphs in the question. In the first part of \(g(x) \), the value of \(g(x)\) is given by the minimum value of \( f \) in the range \( (-3 ,x) \). Since the function is decreasing till \( -1 \), \(g(x) \) matches with \( f(x) \). After that the value of \( g(x) \) becomes a constant equal to \( -1 \) since that is the local minima. Similarly, we can plot it for the positive part. If it still sounds unclear, let me know I'll elaborate further. The answer to the third question should be C.

Sudeep Salgia - 2 years, 4 months ago

Log in to reply

@Sudeep Salgia Why did you graphed a straight line in \((1,2)\) , I was thinking of it to be \(f(x)\).

Kushal Patankar - 2 years, 4 months ago

Log in to reply

@Kushal Patankar It is maximum value of \(f(t) \) where \( 0 \leq t \leq x\). Since the function is decreasing, the value would be \(f(0) \) which is \(0\).

Sudeep Salgia - 2 years, 4 months ago

Log in to reply

@Sudeep Salgia But in \((1,2)\) it is increasing. So all \(f(x)\) will be greater than \(f(t)\).

Kushal Patankar - 2 years, 4 months ago

Log in to reply

@Kushal Patankar Sorry for my misleading statement. It is true that the function is increasing in the interval \((1,2)\) but notice that the value is still negative, that is, \( f(r) < f(0) = 0 \ \ \forall \ r \ \ \in (1,2) \). Since \( t \ \in [0, x] \), therefore \( \forall \ x < 2 , f(0) > f(x) \) .

Sudeep Salgia - 2 years, 4 months ago

Log in to reply

@Sudeep Salgia OK, got you, thanks ☺☺☺

Kushal Patankar - 2 years, 4 months ago

Log in to reply

@Kushal Patankar Happy to help. :)

Sudeep Salgia - 2 years, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...