Derivatives

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What is a derivative?

Back

A derivative represents the rate of change of a function with respect to a variable. It is a measure of how a function's output value changes as its input value changes.

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What does it mean for a function to have a horizontal tangent line?

Back

A function has a horizontal tangent line at a point where the derivative is zero, indicating that the slope of the tangent line is flat.

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How do you find the derivative of a polynomial function?

Back

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What is the power rule for derivatives?

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What is a relative minimum?

Back

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

Front

What is the significance of a derivative changing from positive to negative?

Back

If the derivative changes from positive to negative at a point, it indicates that the function has a relative maximum at that point.

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What is the equation of a tangent line?

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How do you determine if a function has no relative extrema?

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A function has no relative extrema if its derivative is always positive or always negative.

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What does it mean if the derivative of a function is zero?

Back

If the derivative of a function is zero at a point, it indicates that the function has a horizontal tangent line at that point, which could be a relative maximum, minimum, or a point of inflection.

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