Results 1 to 3 of 3

Math Help - derivative of unknown function

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    25

    derivative of unknown function

    Says here, a function f is defined for all real numbers and has the following property: f(a + b) - f(a) = 3(a^2)b + 2b^2. f ' (x) is equal to what?

    Basically, are a and b constants or something? How do I find f ' (x)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,911
    Thanks
    775
    Hello, LeoBloom!

    A function f is defined for all real x and: . f(a + b) - f(a) \;= \;3a^2b + 2b^2

    Find f'(x)
    Recall the defintion: . f'(x) \;=\;\lim_{h\to0}\frac{f(x+h) - f(x)}{h}


    They have given us about half of this defintion: . f(a+b) - f(a) \:=\:3a^2b - 2b^2

    Divide by b\!:\;\;\frac{f(a+b) - f(a)}{b} \;=\;\frac{3a^2b + 2b^2}{b} \;=\;3a^2 + 2b


    Take the limit as b\to0

    . . \underbrace{\lim_{b\to0}\frac{f(a+b) - f(a)}{b}}_{\text{This is }f'(a)} \;=\;\lim_{b\to0}(3a^2 + 2b) \;=\;3a^2

    So we have: . f'(a) \:=\:3a^2


    Therefore: . \boxed{f'(x) \:=\:3x^2}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2008
    Posts
    25
    Wow thanks alot, I can't believe I didn't notice how similar it looked to the definition of a derivative.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Max/Min problem with function unknown.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 18th 2011, 12:33 PM
  2. Unknown Constants Possible Derivative Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 14th 2009, 09:07 AM
  3. Maximums through an unknown function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 29th 2009, 01:42 AM
  4. one to one function with unknown constant!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 6th 2007, 09:26 AM
  5. Gradient of an Unknown Function!!!
    Posted in the Calculus Forum
    Replies: 16
    Last Post: August 1st 2006, 09:32 AM

Search Tags


/mathhelpforum @mathhelpforum