Quiz3%20Solutions

Quiz3%20Solutions - p x = x 3-2 x 1(1-3 x 2-2 x-1 x 3-2 x...

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Math 102 Quiz 3: 12.2 and 12.3 Last Name, First Name: Section: Answer the following questions and show your work. 1. Find the derivative of g ( t ) = 3(5 t 4 + 1 t - 1 t + 9 t 1 3 ) 2. The strength of a patient’s reaction to a certain drug is given by R ( Q ) = Q ± C - Q 3 ² 1 2 where C is a constant. a. Find R 0 ( Q ), the patient’s sensitivity to the drug. b. When C = 25 and Q = 27, is the strength of the patient’s reaction to the drug increasing or decreasing. Explain your answer. 3. Find the equation of the tangent line to p ( x ) = x 3 - 2 x + 1 1 - 3 x 2 - 2 x at x = 1. For the equation of the tangent line, we need slope m = f 0 (1) and a point (1 ,f (1)). 1. Rewrite the term 2 x as 2 x - 1 so that p ( x ) = x 3 - 2 x + 1 1 - 3 x 2 - 2 x - 1 . 2. Take the derivative using the quotient rule:
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Unformatted text preview: p ( x ) = ( x 3-2 x + 1) (1-3 x 2-2 x-1 )-( x 3-2 x + 1)(1-3 x 2-2 x-1 ) (1-3 x 2-2 x-1 ) 2 = (3 x 2-2)(1-3 x 2-2 x-1 )-( x 3-2 x + 1)(-6 x + 2 x-2 ) (1-3 x 2-2 x-1 ) 2 3. Find m by plugging x = 1 into p ( x ): m = p (1) = (1)(-4)-(0)(-4) (-4) 2 =-4 16 =-1 4 4. Find f (1) by plugging x = 1 into p ( x ): p (1) =-4 = 0. 5. Using the slope m =-1 / 4 and the point (1 , 0), find the equation of the line with the point slope formula: y-y 1 = m ( x-x 1 ) which gives y =-1 / 4( x-1)....
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