Thread: Derivative of 1-1 function

I'm having trouble on this problem

Let f(x)= 1/4 x^2 +x-1. This is a 1-1 function and hence its inverse is a 1-1 function. Find the following a. f'(2) b. f'(3)

I got this so far

3/4 x^2 +1 then 3/4 (2)^2 +1 = 3+1 = 4 My first question is am I right by getting the derivative and sub the 2 in? my second question is if I am right then what do i do afterward?

Originally Posted by goldenroll

Let f(x)= 1/4 x^2 +x-1. This is a 1-1 function

Are you sure?

Originally Posted by goldenroll

Find the following a. f'(2) b. f'(3)

Originally Posted by goldenroll

I'm having trouble on this problem

Let f(x)= 1/4 x^2 +x-1. This is a 1-1 function and hence its inverse is a 1-1 function. Find the following a. f'(2) b. f'(3)

I got this so far

3/4 x^2 +1 then 3/4 (2)^2 +1 = 3+1 = 4 My first question is am I right by getting the derivative and sub the 2 in? my second question is if I am right then what do i do afterward?

The way you've writtenthis question confuses me a litle bit. The derivative of a function is not dependent on whether or not it has an inverse.

But if you want , then





A function is said to have an inverse function , if for every element in the range of , there exists one, and only one corresponding element in the domain of

Is the definition satisfied in your case?

Originally Posted by goldenroll

I'm having trouble on this problem

Let f(x)= 1/4 x^2 +x-1. This is a 1-1 function and hence its inverse is a 1-1 function. Find the following a. f'(2) b. f'(3)

No, it's not 1-1 and does not have an inverse. Or are you restricting f to a given interval?

[/quote]I got this so far

3/4 x^2 +1[/quote]
What is equal to this? Certainly Not the derivative! f'(x)= (1/2)x+ 1.

then 3/4 (2)^2 +1 = 3+1 = 4 My first question is am I right by getting the derivative and sub the 2 in? my second question is if I am right then what do i do afterward?