Calculus 3 (10 der 6 int 4 lim)

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What does it mean for a function to be increasing?

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A function is increasing on an interval if its derivative is positive on that interval.

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How do you find the intervals where a function is increasing?

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To find the intervals where a function is increasing, calculate the derivative and determine where it is greater than zero.

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What is the second derivative test?

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The second derivative test is used to determine the concavity of a function and can help identify local maxima and minima.

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What is the limit of a function?

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The limit of a function describes the value that the function approaches as the input approaches a certain point.

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What is the definition of a local maximum?

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A local maximum is a point where the function value is higher than the values of the function at nearby points.

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What is the definition of a local minimum?

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A local minimum is a point where the function value is lower than the values of the function at nearby points.

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What is the relationship between the first derivative and the graph of a function?

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The first derivative indicates the slope of the tangent line to the graph of the function, showing where the function is increasing or decreasing.

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