hw8-24 - 5 x-1 compute and simplify the secant slopes on...

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Math 170-010 Homework 8/24 Fall 2011 (Revised 9:45am 8/24) Goals: Compute lots of algebraic secant slopes. Learn to simplify secants coming from polynomial functions. Learn to simplify secants coming from square root functions. Learn to simplify secants coming from rational functions. Warmup: Factor each expression. Try to create factors of ( x - 2). These will not be turned in with Friday’s homework. 1. x 2 - 4 2. 5 x 2 - 20 3. - 3 x + 6 4. 5 x 2 - 20 - 3 x + 6 5. x 3 - 8 Exercises: These will be turned in on Friday. Keep them organized and in order. 1. An object is thrown into the air. It’s height as a function of time is y ( t ) = 30 t - 16 t 2 where t is in seconds and y is in feet. (a) Compute the average velocity on the interval [1 , a ]. Simplify as far as possible. (b) Compute the average velocity on the interval [1 , 1 + h ]. Simplify as far as possible. 2. For the function f ( x ) = 3 x 2 - 7 x + 5, compute and simplify: (a) Δ f Δ x on [ - 1 , a ]. (b) Δ f Δ x on [ - 1 , - 1 + h ]. 1
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(c) Δ f Δ x on [ a, b ]. 3. For the function g ( x ) = x + 2, compute and simplify: (a) Δ g Δ x on [7 , a ]. (b) Δ g Δ x on [7 , 7 + h ]. 4. For the function h ( x ) =
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Unformatted text preview: 5 x-1 , compute and simplify the secant slopes on the intervals: (a) [3 , a ]. (b) [3 , 3 + h ]. 5. Given y = t 2-√ t + 3 t , compute Δ y Δ t on [2 , a ]. Simplify completely. 6. For f ( x ) = x 3 , compute and simplify at least one of: (a) Δ f Δ x on [2 , a ]. (b) Δ f Δ x on [2 , 2 + h ]. Challenge Problems: 1. Find and simplify the secant slope of y = 1 √ x on [4 , a ]. 2. Find and simplify the secant slope of y = x 3 / 2 on [4 , a ]. 2 Hints and Answers Warmup: 1. ( x-2)( x + 2) 2. 5( x-2)( x + 2) 3.-3( x-2) 4. 5( x-2)( x + 2)-3( x-2) 5. ( x-2)( x 2 + 2 x + 4) Exercises: 1. (a) 14-16 a ; (b)-2-16 h . 2. (a) 3 a-10; (b) 3 h-13; (c) 3 a + 3 b-7. 3. (a) 1 3 + √ a + 2 ; (b) 1 3 + √ h + 9 . 4. (a)-5 2( a-1) ; (b)-5 2(2 + h ) . 5. a + 2-1 √ a + √ 2-3 2 a 6. Either a 2 + 2 a + 4 or 12 + 6 h + h 2 . Challenge Problems: 1.-1 2 √ a (2 + √ a ) 2. a 2 + 4 a + 16 a 3 / 2 + 8 3...
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hw8-24 - 5 x-1 compute and simplify the secant slopes on...

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