# Derivative of 1-1 function

• July 28th 2009, 10:19 PM
goldenroll
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?
• July 28th 2009, 10:27 PM
pickslides
Quote:

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

Are you sure?

Quote:

Originally Posted by goldenroll
Find the following a. f'(2) b. f'(3)

$f'(x) = \frac{x}{2}+1$

$f'(2) = \frac{2}{2}+1 = \dots$

$f'(3) = \frac{3}{2}+1 = \dots$
• July 28th 2009, 10:31 PM
VonNemo19
Quote:

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 $f'(2)\text{ and }f'(3)$, then

$f'(x)=\frac{1}{2}x+1\Rightarrow{f'(2)}=2\text{ and }f'(3)=\frac{5}{2}$

A function $f$ is said to have an inverse function $f^{-1}$, if for every element in the range of $f$, there exists one, and only one corresponding element in the domain of $f$

Is the definition satisfied in your case?
• July 29th 2009, 07:07 AM
HallsofIvy
Quote:

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.

Quote:

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?