Why second derivative is negative at Maxima or Why second derivative is positive at minima?

what happens when the second derivative is positive? negative?

Second Derivative Test

What the Second Derivative Tells Us

Max and Min and Second Derivative

Relative Extrema, Local Maximum and Minimum, First Derivative Test, Critical Points- Calculus

Concavity, Inflection Points, and Second Derivative

2nd derivative test, a visual explanation

3.2 - Using Second Derivatives to Classify Max and Min Values

Learn how to use the second derivative test to determine relative extrema

Use the Second Derivative Test to Find all Relative Extrema f(x) = x^3 - 3x^2 + 2

Geometry of the Derivatives (4 of 6: Determining max/min with second derivative)

Second Derivative Test to Determine Maximum and Minimum Values

Calculus: Why you should NOT use second derivative test to find local max/min and what to do instead

Second Derivative Test - Why and How?

Concavity, Inflection Points, Increasing Decreasing, First & Second Derivative - Calculus

Lesson: The Second Derivative Test for Extrema

3.4D Applications of the Second Derivative (Max or Min, Concavity, Points of Inflection)

Section 2.4.2 - First and Second Derivatives as Positive, Negative, and Zero (Graph)

Find critical numbers and use second 2nd derivative test to determine maximum or minimum.