hw9-9 - Math 170-010 Homework 9/6 Fall 2011 Goal: Compute...

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Math 170-010 Homework 9/6 Fall 2011 Goal: Compute derivatives of all powers of x . Notice the recurring pattern that results from factoring a diFerence of powers: you get “some number of copies of some object raised to some power.” Exercises: NOTE: My directions strongly suggest doing these problems with x and u . If you prefer to use x and x + h , I don’t mind. Try to build tables like mine, but expect that your algebra will look diFerent than mine. 1. Consider the function f ( x ) = x 2 . (a) Using ±xed end x and free end u write down the secant slope. (b) ²actor this, aiming to cancel ( x - u ). (c) Let u x to get tangent slope. (d) Assemble your answers in a table that looks like this: ²unction Secant ²actored Tangent x 2 x 2 - u 2 x - u ( x - u )( x + u ) x - u 2 x 2. Repeat for the function f ( x ) = x 3 . Add another line to the table. HINT: DiFerence of cubes factors as ( x 3 - u 3 ) = ( x - u )( x 2 + ux + u 2 ). 3. Repeat for the function f ( x ) = x 4 . Add another line to the table. HINT: DiFerence of fourth powers factors as ( x 4 - u 4 ) = ( x - u )( x 3 + x 2 u + xu 2 + u 3 ). 4. Repeat for the function f ( x ) = x 5 . You might be able to guess how to factor ( x 5 - u 5 ) now. If not, google it. But then you have to try x 6 on your own. 5. Look at your table and see if you can guess the answers to the following questions. (a) What would the factored secant slope look like for
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This note was uploaded on 10/11/2011 for the course MATH 170 taught by Professor Staff during the Fall '08 term at Boise State.

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hw9-9 - Math 170-010 Homework 9/6 Fall 2011 Goal: Compute...

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