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Warm up Problem If , find

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**The Derivative Function**

Def. For any function f (x), we can find the derivative function f (x) by:

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**Ex. Given the graph of f (x), sketch f (x).**

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**Ex. Given the graph of f (x), sketch f (x).**

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Note: f (a) is a number f (x) is a function Algebraically Ex. If f (x) = 5, find f (x).

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**Ex. If f (x) = 3x – 2, find f (x).**

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Ex. If f (x) = x2, find f (x).

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**Pract. If f (x) = x3, find f (x).**

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Rules If f (x) = constant, then f (x) = 0. If f (x) = mx + b, then f (x) = m. If f (x) = xn, then f (x) = nxn – 1. Only use these rules, don’t make up your own. If the problem says “Use definition of derivative”, you must use the limit.

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Ex. If f (x) = x902, find f (x). Note: A function is differentiable at a point if the function and its derivative are continuous at the point.

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**Ex. Is the function differentiable at x = 2?**

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