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Published byTamsyn Jones Modified over 9 years ago
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Differentiability and Rates of Change
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To be differentiable, a function must be continuous and smooth. Derivatives will fail to exist at: cornercusp vertical tangent discontinuity (jump)
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True/False : 1)If a function is differentiable, then it must be continuous. give and example 2) If a function in continuous, then it must be differentiable. give an example
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2) 1)
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Recall the connection between average rate of change an instantaneous
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Review: average slope: slope at a point: average velocity: (slope) instantaneous velocity: (slope at 1 point) If is the position function: These are often mixed up by Calculus students! So are these! velocity = slope
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The slope of a curve at a point is the same as the slope of the tangent line at that point. If you want the normal line (perpendicular line), use the negative reciprocal of the slope.
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7) 8)
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