True-False Quiz Question 13: Determining Derivatives via Coefficients of a Power Series

In this video I show that we can solve for any given derivative of a function just by looking at its coefficients if it can be written as a convergent power series. The coefficients of a power series are given by the formula: (n-th derivative at a) / n!. In our question, we are asked to solve for the 3rd derivative of such a function. I show that we can solve it via the coefficients of a power series, and then confirm our result by solving for the derivatives directly. Thus, the answer to the question is True.

Time stamps:

- Question 13: 0:00
- Solution 1: True. Coefficients of a Power Series: 0:27
- n=3 coefficient: 3:15
- Solution 2: Differentiating f(x) directly: 4:32
- Third derivative is 2: 6:27

Full video below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

Related Videos:

Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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