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Description of Directional Derivative.

The dot product (often referred to as the inner product in a Linear Algebra text) is a useful tool in developing several important techniques of multivariable calculus. Your task is to give a detailed description of why the gradient points in the direction of the maximum increase of a function. You may restrict your essay to R3. The essay should include
1) a definition and description of the directional derivative
2) how the dot product can be used to justify that the gradient points in the direction of maximum of a function.

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