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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online