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Unformatted text preview: is a fairly “wild” function. Find the xvalues of its horizontal tangent lines and show there are inﬁnitely many of them on the interval (0 , 1). (Hint: to ﬁnd where f ( x ) = 0, use the idea of Project 1.) 3. For which of these functions would logarithmic diﬀerentiation truly be beneﬁcial/necessary? x e x 2 ln( x 2 e x 2 ) x 2 + e x 2 x 2 e x 2 4. Examine the function f ( x ) = xe 1 2 ( x2) 2 ( x + 2) 3 . Calculate f ( x ) using chain, power, and exponential rules for diﬀerentiation but DO NOT try to simplify. This time use logarithmic diﬀerentiation to calculate the derivative of f ( x ). At what values does logarithmic diﬀerentiation fail? What is the slope of the tangent line to f ( x ) at x = 2? x = 0? Where does f ( x ) have horizontal tangent lines (add up your fractions. ..)?...
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 Fall '08
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 Calculus, Derivative, Slope, Continuous function

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