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

👉 Learn how to find the extrema of a function using the second derivative test. The second derivative test states that if a function has a critical point for which f'(x) = 0, and the second derivative is positive, then the function has a minimum point at that point. If the second derivative is negative, then the function has a maximum point at that point and if the second derivative is zero, then the function has an inflection point at that point.

To find the extrema of a function using the second derivative test, we first find the derivative of the function and equate it to zero. Then, we solve the resulting equation for x to get the critical points. Then take the second derivative of the function and substitute each of the critical points into the second derivative. The critical points for which the second derivative is positive represent minimum points, the critical points for which the second derivative is negative represent maximum points, while the critical points for which the second derivative is zero represent inflection points.

Organized Videos:
✅Applications of the Derivative
✅Determine Increasing or Decreasing Function From a Table
✅Concavity of Functions
✅Extreme Value Theorem of Functions
✅First Derivative Test for Functions
✅Find the Critical Values of a Function
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
✅Sketch the Graph of the First and Second Derivative
✅Find the Points of Inflection of a Function
✅Second Derivative Test For a Function
✅Intermediate Value Theorem of Functions

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[ambassadorforchrist]

brief, precise and to the point = excellent video. Thanks

[katherinemoran]

You're the only reason I'm passing calc

[tully]

If anyone see this lol why is -3/2 > 0 isn’t less than bc it’s a negative

[erincontreras]

how would you solve if it is g(x)= (x-2)^2/x-4?

[gabbyalomon]

you don't even explain what you're doing??