Calculus 3 (10 der 6 int 4 lim)

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How do you determine where a function is increasing?

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A function is increasing where its derivative is positive.

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Front

What is the second derivative test?

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The second derivative test helps determine the concavity of a function and can indicate local maxima or minima.

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What does it mean for a function to be concave up?

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A function is concave up if its second derivative is positive, indicating that the slope of the tangent line is increasing.

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What does it mean for a function to be concave down?

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A function is concave down if its second derivative is negative, indicating that the slope of the tangent line is decreasing.

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What is the formula for finding the derivative of a polynomial function?

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This interval indicates where the function is increasing.

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What is the first derivative test?

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The first derivative test is used to determine whether a critical point is a local maximum, local minimum, or neither.

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What is the relationship between the first derivative and the slope of the tangent line?

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The first derivative at a point gives the slope of the tangent line to the function at that point.