Understanding 1st & 2nd Derivative Tests for Finding Extrema

Jan 03, 2026

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Explore the fundamental concepts of the first and second derivative tests in calculus. This discussion covers defining these tests and how to apply them to identify extrema of functions. Learn to maximize or minimize quantities by formulating functions in one variable, setting derivatives equal to zero to find critical numbers, and recognizing where derivatives do not exist. Utilize both derivative tests effectively, while ensuring to review endpoint values. Ready to solidify your understanding? Engage with your homework assignments and have a productive weekend!

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Understanding 1st & 2nd Derivative Tests for Finding Extrema

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Presentation Transcript

Did you Check your Endpoints? 1st & 2nd Derivative Tests Today you will apply and formally define the first and second derivative tests.
Discussion

1st Derivative Test
2nd Derivative Test

Solving Extrema Problems • Identify the quantity to maximize or minimize and formulate a function in terms of one variable. • Set the derivative equal to 0 to find the critical numbers. Be sure to look for x-values where the derivative does not exist since critical numbers may occur at those places. • Use either the first or second derivative test for extrema and be sure to check the endpoints.
Assignment HW Q Have a nice weekend!