Help: Critical points

f(x)=(a23a+2)(cos2x4sin2x4)+(a1)x+sin1f\left( x \right) =\left( { a }^{ 2 }-3a+2 \right) \left( \cos ^{ 2 }{ \frac { x }{ 4 } } -\sin ^{ 2 }{ \frac { x }{ 4 } } \right) +\left( a-1 \right) x+\sin { 1 }

The set of all values of aa for which the function above does not posses critical point is __________\text{\_\_\_\_\_\_\_\_\_\_} .

Note by Akhilesh Prasad
3 years, 8 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

What's the answer ?? I'm getting a€(0,4)- {1} ........... I might have missed cases because I'm a expert in doing that.. ;-)

Rishabh Jain - 3 years, 8 months ago

Log in to reply

The answer given is (1,)(1,\infty).

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

How you solved ?? I found f'(x) and ensured that it does not vanish!! And ultimately got the wrong answer!!

Rishabh Jain - 3 years, 8 months ago

Log in to reply

@Rishabh Jain Hey were u able to open the file i uploaded. coz it was on google drive

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

@Rishabh Jain Finally, found it My solution

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

@Akhilesh Prasad And shouldn't where you multiplied inequality by (a-2) cases must be made for a-2>0 and a-2<0??

Rishabh Jain - 3 years, 8 months ago

Log in to reply

@Rishabh Jain Considered the cases you told me to, still i am not getting the desired answer. Corrected solution part 1

Corrected solution part 2

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

@Akhilesh Prasad So we both are getting the same answer that is not correct!! ... ??

Rishabh Jain - 3 years, 8 months ago

Log in to reply

@Rishabh Jain On a side not, I would wanna ask you are you gonna give JEE this year.

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

@Akhilesh Prasad absolutely Yes!!

Rishabh Jain - 3 years, 8 months ago

Log in to reply

@Akhilesh Prasad Should at the end cases be like:
(1) Right Max value<0
(2) Left Min value>0

Rishabh Jain - 3 years, 8 months ago

Log in to reply

@Rishabh Jain It's too time consuming writing the whole answer so i wanted to attach the scan of the hand written answer, but i dunno how to do it, if you could tell me how to do it.

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

@Rishabh Cool, I have got a issue in this one too so if you will please, see this one too

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

@Rishabh Cool. Would you spare some of your time to please post a solution of this.

Akhilesh Prasad - 3 years, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...