MHB Confused: Seeking Help on Problem Solution

  • Thread starter Thread starter Albert Einstein1
  • Start date Start date
  • Tags Tags
    Confused
Click For Summary
The discussion revolves around a user seeking validation for their problem-solving approach. They express uncertainty about whether they solved the problem correctly and request feedback on their reasoning. A response highlights a mistake in the user's bounding, specifically stating that $x^2(x^2 - 2)$ is less than or equal to $-x^2$. Another response confirms that the user's second assertion is correct. Overall, the conversation focuses on clarifying the user's understanding of their solution.
Albert Einstein1
Messages
3
Reaction score
0
I am not entirely sure if I solved this problem correctly. Please let me know if my reasoning is flawed. Thank you and I appreciate your help greatly.
 

Attachments

  • C81A8208-41D5-4B0B-8574-30C16FD7F3C3.jpeg
    C81A8208-41D5-4B0B-8574-30C16FD7F3C3.jpeg
    42 KB · Views: 125
  • 50D89683-48F0-4EC5-9C90-EB3D3BB43619.jpeg
    50D89683-48F0-4EC5-9C90-EB3D3BB43619.jpeg
    285.8 KB · Views: 134
Physics news on Phys.org
Albert Einstein said:
I am not entirely sure if I solved this problem correctly. Please let me know if my reasoning is flawed. Thank you and I appreciate your help greatly.
 

Attachments

  • 1CC00144-1DF9-4A5D-95B4-E3D42947A0F3.jpeg
    1CC00144-1DF9-4A5D-95B4-E3D42947A0F3.jpeg
    110.5 KB · Views: 118
In the first, post your "bounding" is wrong. $x^2(x^2- 2)$ is less than or equal to $-x^2$.

For the second, yes, that is correct.
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
View full post »

Similar threads

MHB Double-Check My Problem Solving | Correct Reasoning Verification
  • · Replies 3 ·
Replies
3
Views
1K
Spherical pendulum confusion [Issue resolved]
  • · Replies 2 ·
Replies
2
Views
621
MHB Integration Help: Struggling with Distance Qn
  • · Replies 4 ·
Replies
4
Views
1K
MHB What Is the Total Distance Traveled by the Particle from t = 0 to t = 3?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Need help with a work related math problem
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Solve Chain Rule Confusion with Diff. Eq. | Help
  • · Replies 10 ·
Replies
10
Views
2K
MHB Integrating a piecewise function?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Working out where a function is non-negative
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding Maximum Value of an Expression with Respect to $x$
  • · Replies 7 ·
Replies
7
Views
3K
MHB Find the area by using disk method
  • · Replies 4 ·
Replies
4
Views
1K