#Week 5: Concavity and Second Derivative Test

[math-learning-journey-blog]

✨4QW5: Concavity and Second Derivative Test ✨

My opinions on this topic are identical to those I had on the last one. It's essentially an application of the second derivative test, which I didn't believe had any practical purpose other than allowing derivatives of derivatives. I particularly appreciate the fact that the 2nd derivative test may be used to detect relative extrema. The examples provided are each distinctive in their own way, which will come in handy when I'm faced with various types of problems during the long test.

Overall, I feel the learning guides will be sufficient in assisting with the topic.

*Picture 1 example solution sa sync meet

*Picture 2 sync meet

[m47h-2]

📖Blog Entries #5 & #6: Concavity, Second Derivative Test & Sketching of Graphs using Derivatives

FOURTH QUARTER: Weeks 5 and 6

Hi, so...welcome back to my channel, CHAROT AHHAHA. Welcome and for this vlog I’ll be talking about what I think about these two last lessons for the 4th quarter and this school year. And yes, this is going to be my last blog here in my account(I think, maybe hahaha). Anyways, lets make this worthwhile. ENJOY!

❓REVIEW

For the Second Derivative Test, the graph of the function determines the concavity. It said that a function is concave up if its second derivative value is greater than 0, while for concave down, its the opposite. Another thing about the second derivative test is that it determines the possible points of inflection which is/are point/s that the function changes concavity. 

For sketching the graphs, there is a process:

1. Find the f’(x) and f’’(x) of a function

2. Solve for critical numbers of the function wherein it/they make/s the f’(x) = 0

3.  Solve for the possible points of inflection wherein f’’(x) = 0

4. Create a table of signs

5. Conclusion on what behavior does each interval makes

6. Sketch your graph/s

These are my notes and practice sheets:

(I was able to understand about the first and second derivative tests more because of the table of signs. Like seriously though, before this topic, I’m having a hard time about relative max and min.)

💯ENDING REMARKS

First of all, I want to thank my Math teachers especially Sir Ric for teaching us and being patient. Second, I also want to thank my family for being supportive for me in my studies and trying to understand what I’m going thru. Another is my friends and fellow classmates that help me in understanding some lessons that I have hard time understanding. And lastly, the Lord for always being on my side and as a person who I can talk to whenever I feel tired and depressed. This school year has really been a full-on-course rollercoaster ride for me. I’ve learned a lot and matured over the school year. For what I have learned from Math Level 2, I will carry it on to the next school level (Hopefully maremember ko pa hahaha) and when going to college which is soon na. Anyways, this has been a journey for me. It has been fun while it lasted. See you all and BYEEEEEEEEEEEEEE!✨🎉🎇🎆🎊

(Once again, thank you...next - iah💝)

[eberliiii]

Blog Post # 31: Concavity and Second Derivative Test

May 26, 2022, 5:23 PM (GMT + 8)

The lesson for week 4.6 in Mathematics 5 was relatively easy with the help of the examples provided in the module. It was also relatively similar to the previous topic, which made it easier than expected. Although solving its problems was a little lengthy, it wasn’t challenging. The images below are proof of my notes on the subject matter. 

The image above contains part 1 of my notes on Concavity and the Second Derivative Test.

The image above contains part 2 of my notes on Concavity and the Second Derivative Test.