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Math121SampleQuiz2Sols

Math121SampleQuiz2Sols - QUIZ#2(SAMPLE QUESTIONS PART 1(NO...

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QUIZ #2 (SAMPLE QUESTIONS) PART 1 (NO CALCULATORS!) 1) Let f x x x ( ) = + 4 1 2 . Find ¢ ( ) f x . Simplify your answer. (6 points) ¢ ( ) = ( ) - ( ) ( ) = + ( ) ( ) - ( ) + ( ) + ( ) = + ( ) ( ) - ( ) ( ) + ( ) = + - + ( ) = - + ( f x x D x x D x x x x x x x x x x x Lo D Hi Hi D Lo the square of what© s below Quotient Rule 2 2 2 2 2 2 2 2 2 2 2 1 4 4 1 1 1 4 4 2 1 4 4 8 1 4 4 1 2 2 x x ) 2 Note 1: Factoring the numerator does not lead to further simplification in this case. Note 2: You could have rewritten f x ( ) as 4 1 2 1 x x + ( ) - and then used the Product and Generalized Power Rules. However, the simplification would have been trickier. 2) Let f x x x ( ) ( ) = + 6 4 3 1 . Find ¢ ( ) f x . Simplify your answer. Do not expand out powers; for example, don't work out 3 1 4 x + ( ) . (6 points) First, use the Product Rule. ¢ ( ) = [ ] + ( ) [ ] + ( ) [ ] + ( ) [ ] = [ ] + ( ) È Î Í Í ˘ ˚ ˙ ˙ + [ ] + ( ) [ ] ( ) = + ( f x x D x D x x x x x x D x x x x 6 4 6 4 6 3 5 4 3 1 3 1 4 3 1 3 6 3 1 3 1 Use the Generalized Power Rule. tail Note: 3 is the tail, because it is + . 1 2 44 3 44 { 12 3 1 6 x x ) + + ( ) 3 5 4 6 3 1 x x
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3) Let y x = 3 . Find d y dx x 2 2 8 = . (9 points) In other words, find ¢¢ ( ) f 8 , where y f x
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