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Math Help - Derivative of 1-1 function

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by goldenroll View Post
    Let f(x)= 1/4 x^2 +x-1. This is a 1-1 function
    Are you sure?

    Quote Originally Posted by goldenroll View Post
    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
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by goldenroll View Post
    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?
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  4. #4
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    Quote Originally Posted by goldenroll View Post
    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?
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