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Derivative as a Function
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Example For find the derivative of f and state the domain of f’
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The derivative can be regarded as a new function
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Example Given the graph of the function, f , sketch the graph of f’
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Example If find a formula for f’(x). Graph both functions on the calculator and compare.
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Differentiable A function is said to be differentiable at a is f’(a) exists. It is differentiable on an open interval (a,b) if it is differentiable at every number on that interval. If a function is differentiable at a, then it is continuous at a Some functions can be continuous, but still not differentiabl
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Example Where is differentiable.
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Functions that are NOT differentiable
Graphs with kinks or corners do not have tangents at the kinks, so they are not differentiable Functions that have jump discontinuities at a point are not differentiable at that point If a tangent line to a function is vertical at a point, the function is not differentiable at that point
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