2.2 Class Notes - The first question on the prelim(4 points...

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The first question on the prelim (4 points) Write your name and section number on your paper. There will be three word problems (not counting this one) Equation of the tangent line 1/3 1/3 Find the equation of the tangent line to ( ) at 216. Use the tangent line to estimate (225) Give the answer to four decimal places f x x x = = 0 0 0 ( ) '( )( ) y f x f x x x = + 1/3 2/3 2 0 0 0 1/3 1/3 ( ) '( ) (1/3) 216 ( ) 6 '( ) 1/(3 6 ) 1/108 6 ( 216)/108 9 1 (225) 6 6 6.0833 108 12 (225) exp((1/3)ln(225)) 6.0822 f x x f x x x f x f x y x = = = = = = = + + = + = = = Monkeyface prickelback / 4 2.5 16(1 ) inches 0.01 pounds Find / t L e W L dW dt = = / 4 2.5 1.5 / 4 / 4 1.5 / 4 / 4 1.5 / 4 16(1 ) 0.01 / 0.025 / (16)(1/ 4) / 0.025[16(1 )] 4 0.64(1 ) t t t t t t L e W L dW dL L dL dt e dW dt e e e e = = = = = = dW dW dL dt dL dt = Solution 2 / 4 2.5 / 4 2.5 / 4 1.5 / 4 / 4 1.5 / 4 16(1 ) inches 0.01 pounds Find / ( ) 0.01(16(1 )) '( ) 0.01(2.5)(16(1 )) (4 ) 0.64(1 ) t t t t t t L e W L dW dt W t e W t e e e e = = = = =
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