Results 1 to 3 of 3

Thread: Find the function.

  1. #1
    Nov 2010

    Find the function.

    Find the function with the given derivative whose graph passes through the point P.

    1.) $\displaystyle f'(x)=sin(x)+cos(x), P(\pi,3)$
    2.) $\displaystyle f'(x)=x^\frac{1}{3}+x^2+x+1, P(1,0)$

    Can someone please explain what I have to do here. I'm pretty sure it involves anti-derivatives, but I've never done them before. If you could, could you explain step by step how to do them. Any help is appreciated, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Jun 2009
    United States
    Yes, you basically need to integrate. If you've never done an antiderivative before, then I suggest you look at a tutorial like this:

    Pauls Online Notes : Calculus I - Integrals

    For the first one you have:

    $\displaystyle \int[sin(x)+cos(x)]dx = -cos(x)+sin(x)+C$

    If you differentiate the right side, you'll get the left side for any value of C, which is a constant. The point $\displaystyle (\pi,3)$ allows you to find C so you can determine the exact function:

    $\displaystyle 3=-cos(\pi)+sin(\pi)+C$

    Solve for C...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Dec 2008
    Here are three hints for the first problem:

    $\displaystyle \begin{aligned}
    \frac{d}{dx}(-\cos x)=-(-\sin x)&=\sin x\\
    \frac{d}{dx}\sin x&=\cos x\\
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 14
    Last Post: Jan 18th 2010, 06:16 PM
  2. Find a Function
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 7th 2008, 05:08 AM
  3. HELP!! Find f(x) for the given function...
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Sep 15th 2008, 03:15 PM
  4. Replies: 3
    Last Post: Jul 17th 2007, 11:06 AM
  5. Find a function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Dec 2nd 2006, 01:49 AM

Search Tags

/mathhelpforum @mathhelpforum