ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

5.7 Using the Second Derivative Test to Determine Extrema

#secondderivative

#extrema

โฑ๏ธย ย 1 min read

written by

Sumi Vora

sumi vora

June 8, 2020


๐ŸŽฅWatch: AP Calculus AB/BC - Concavity and f, f', f''

Using the Second Derivative Test

If we combine our knowledge of first derivatives and second derivatives, we find that we can use the second derivative to determine whether a critical point is a relative minimum or relative maximum.ย โ—๏ธ

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(555).png?alt=media&token=267258be-fb61-4885-816b-241e195dcde0

In other words, if we know that there is a local extreme at a certain point and the graph is concave up at that point, it must be a minimum, and, if the graph is concave down at that point, it must be a maximum. ๐Ÿ™‹โ€โ™‚๏ธ

Example Problems

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(557).png?alt=media&token=aab95edc-0f28-4536-aecf-57fb3f325e26

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(559).png?alt=media&token=942c24a2-a078-486d-bcf7-fed0745e0647

We can find the critical points of implicit functions in a similar manner. The critical points occur when dy/dx = 0.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(562).png?alt=media&token=87671976-7757-4cd8-97df-c2864c434bb5

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(563).png?alt=media&token=451d6dc3-522f-408e-aa0b-a0b51cae8f6e

ย 

continue learning

Slide 1 of 10
Fiveable

Join Our Community

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

Fiveable Logo

2550 north lake drive
suite 2
milwaukee, wi 53211

92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2020 | all rights reserved.