What are some examples of extrema in functions?
An example of an AI chatbot conversation about identifying extrema in mathematical functions.
What are some examples of extrema in functions?
Extrema refer to the maximum and minimum values of a function. For example, the function f(x) = -x^2 has a maximum at (0,0).
Can you give me another example?
Sure! The function f(x) = x^3 - 3x has a local maximum at (-1, 2) and a local minimum at (1, -2).
How do you find these extrema?
To find extrema, you can use calculus. First, take the derivative of the function, set it to zero, and solve for x. Then, use the second derivative test to determine if it's a max or min.
What about functions with no extrema?
An example is f(x) = e^x, which is always increasing and has no maximum or minimum.
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