121616949-math.70 - 56 Chapter 3 Rules For Finding...

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56 Chapter 3 Rules For Finding Derivatives Exercises Find the derivatives of the functions in 1–4 using the quotient rule. 1. x 3 x 3 - 5 x + 10 2. x 2 + 5 x - 3 x 5 - 6 x 3 + 3 x 2 - 7 x + 1 3. x 625 - x 2 4. 625 - x 2 x 20 5. Find an equation for the tangent line to f ( x ) = ( x 2 - 4) / (5 - x ) at x = 3. 6. Find an equation for the tangent line to f ( x ) = ( x - 2) / ( x 3 + 4 x - 1) at x = 1. 7. Let P be a polynomial of degree n and let Q be a polynomial of degree m (with Q not the zero polynomial). Using sigma notation we can write P = n X k =0 a k x k , Q = m X k =0 b k x k . Use sigma notation to write the derivative of the rational function P/Q . 8. The curve y = 1 / (1 + x 2 ) is an example of a class of curves each of which is called a witch of Agnesi . Sketch the curve and find the tangent line to the curve at x = 5. (The word witch here is a mistranslation of the original Italian, as described at http://mathworld.wolfram.com/WitchofAgnesi.html and http://instructional1.calstatela.edu/sgray/Agnesi/ WitchHistory/Historynamewitch.html .) 9. If f (4) = 5,
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