What is the first derivative test in calculus?
An example of an AI chatbot conversation about the first derivative test in calculus.
What is the first derivative test in calculus?
The first derivative test is a method used to determine the local maxima and minima of a function by analyzing its first derivative.
How do I apply the first derivative test?
To apply the first derivative test, you find the critical points by setting the first derivative to zero and then test the intervals around these points.
Can you give me an example of using the first derivative test?
Sure! For the function f(x) = x^3 - 3x^2, the first derivative is f'(x) = 3x^2 - 6. Setting this to zero gives critical points at x = 0 and x = 2.
What do I do after finding the critical points?
After finding the critical points, you test the sign of the first derivative in the intervals around these points to determine if they are local maxima or minima.
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