Derivative as a Function

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Presentation transcript:

Derivative as a Function

Example For find the derivative of f and state the domain of f’

The derivative can be regarded as a new function

Example Given the graph of the function, f , sketch the graph of f’

Example If find a formula for f’(x). Graph both functions on the calculator and compare.

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

Example Where is differentiable.

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