2.1 Definition of Derivative

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What does the derivative represent in calculus?

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The derivative represents the slope of the tangent line to the graph of a function at a given point.

Front

What is the limit definition of the derivative?

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What is a tangent line?

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A tangent line is a line that touches a function at a given point and has a slope equal to the instantaneous rate of change of the function at that point.

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What is a normal line?

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A normal line is a line that is perpendicular to the tangent line at a given point on the function.

Front

How do you find the derivative of a function at a specific point using limits?

Back

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What is the relationship between the derivative and the slope of a curve?

Back

The derivative at a point gives the slope of the tangent line to the curve at that point, indicating the rate of change of the function.

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If f'(x) > 0, what does this indicate about the function f?

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If f'(x) > 0, it indicates that the function f is increasing at that point.

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If f'(x) < 0, what does this indicate about the function f?

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If f'(x) < 0, it indicates that the function f is decreasing at that point.

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What does it mean if f'(x) = 0?

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If f'(x) = 0, it indicates that the function f has a critical point, which could be a local maximum, local minimum, or a point of inflection.

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