5.4 Assignment

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What is a critical point in calculus?

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A critical point occurs where the first derivative of a function is zero or undefined, indicating potential relative extrema.

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What is the first derivative test?

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The first derivative test is a method used to determine whether a critical point is a relative maximum, minimum, or neither by analyzing the sign of the derivative before and after the point.

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What is a relative maximum?

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A relative maximum is a point where the function value is higher than all nearby points.

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What is a relative minimum?

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A relative minimum is a point where the function value is lower than all nearby points.

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How do you find the relative extrema of a function?

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To find relative extrema, identify critical points using the first derivative, then apply the first derivative test.