Thread: Difference quotient

Using the conjecture that d/dx*x^n=nx^n-1 for positive integer values of n. In this problem we look at negative values of n instead.

Let f(x)= x^-1.

(a) write the difference quotient for f(x).

(b) Let the change of x= .01. Use the table command on your calculator to build a table of values for the difference quotient.

-Compare the values in your table to the values of -1*x^-2. Can you guess what f'(x) might be based on your table of values?

x diff quotient -1*x^(-2)
-4
-2
-1
-1/2
-1/3

I am not sure how to go about this problem is the difference quotient for part a d/dx*x^-1=nx^-1-1?

If someone can help me understand the quotient I am suppose to use and ow i Use it in part b I think I can figure out the table on my own.
I know the difference quotient how do i use the equation with the d variable or do i even use it?

Originally Posted by asweet1

Using the conjecture that d/dx*x^n=nx^n-1 for positive integer values of n. In this problem we look at negative values of n instead.

Let f(x)= x^-1.

(a) write the difference quotient for f(x).

(b) Let the change of x= .01. Use the table command on your calculator to build a table of values for the difference quotient.

-Compare the values in your table to the values of -1*x^-2. Can you guess what f'(x) might be based on your table of values?

x diff quotient -1*x^(-2)
-4
-2
-1
-1/2
-1/3

I am not sure how to go about this problem is the difference quotient for part a d/dx*x^-1=nx^-1-1?

If someone can help me understand the quotient I am suppose to use and ow i Use it in part b I think I can figure out the table on my own.

difference quotient ...

I know the difference quotient but my question is if i use the equation with the d variable in these problems?

Originally Posted by asweet1

I know the difference quotient but my question is if i use the equation with the d variable in these problems?

no ... you're only confirming that the conjecture works with negative values of n.