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Directions Consider the following function f a at a 2 Part 1 Difference Quotient If...

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Calculus

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Directions Consider the following function f a at a 2 Part 1 Difference Quotient If h0 then the difference quotient can be simplified into the form 2 A f 2 h where A B and C are all non negative constants Find these constants A 2 and B49 and C 14 Note It s possible for one or more of these constants to be 0 1 f x 2x 3 2 f 2 49 Part 2 Derivative Use the simplified expression from Part 1 to then calculate the derivative f 2 B Ch f 2 49 B Ch f 2 lim A A 2 and B 49 and C 14 Note It s possible for one or more of these constants to be 0 That is note the negative in front f 2 h f 2 h Part 2 Derivative Use the simplified expression from Part 1 to then calculate the derivative f 2 f 2 lim h0 Part 3 Tangent Line Find the equation of the tangent line to the curve y f a at a 2 Tangent Line y f 2 h f 2 h

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