Results 1 to 4 of 4

Thread: Derivative

  1. #1
    Member
    Joined
    Nov 2006
    From
    San Francisco
    Posts
    145

    Derivative

    I'm having trouble finding the answer to this problem. : Find the derivative of the function 1/((the square root of(x)) and the equation of the line that is tangent to the graph of f and parallel to the given line 3x-y+1. I also found the answer to this one but it was kind of guess and check. : find the equations of two tangent lines to the graph of f that pass through the indicated point where f(x)=x^2 and the indicated point is (1, -3). The last question i have is how you guys put square roots and other symbols in. Can't seem to find them. Thanks a lot.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by jarny View Post
    I'm having trouble finding the answer to this problem. : Find the derivative of the function 1/((the square root of(x)) and the equation of the line that is tangent to the graph of f and parallel to the given line 3x-y+1. I also found the answer to this one but it was kind of guess and check. : find the equations of two tangent lines to the graph of f that pass through the indicated point where f(x)=x^2 and the indicated point is (1, -3). The last question i have is how you guys put square roots and other symbols in. Can't seem to find them. Thanks a lot.
    The line $\displaystyle 3x-y+1=0$ can be expressed as $\displaystyle y = 3x +1$. A parallel lines means the derivative has slopt $\displaystyle 3$. Thus at which point is the derivative equal to 3?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    From
    San Francisco
    Posts
    145
    Don't need an answer to the first one. I made a simple algebraic mistake which messed up a rather easy problem. Thanks for the answer to the second. Rather moronic of me not to see that Man that was stupid. That was a 1st grade level mistake. Just having a bad day thinking i guess. Can anyone tell me how to make the symbols though?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by jarny View Post
    find the equations of two tangent lines to the graph of f that pass through the indicated point where f(x)=x^2 and the indicated point is (1, -3).
    $\displaystyle y = x^2$

    $\displaystyle \Rightarrow y' =2x$

    so the slope of any tangent line is given by $\displaystyle 2x$

    By the point-slope form, lines passing through $\displaystyle (1,-3)$ have the form:

    $\displaystyle y + 3 = m(x - 1)$

    $\displaystyle \Rightarrow y = mx - (m + 3)$

    but we want lines where the slope is given by $\displaystyle 2x$, so set $\displaystyle m = 2x$, we get:

    $\displaystyle y = 2x^2 - (2x + 3) = 2x^2 - 2x - 3$

    furthermore, we want lines that intersect with $\displaystyle y = x^2$, so equate the two functions. we get:

    $\displaystyle x^2 = 2x^2 - 2x - 3$

    $\displaystyle \Rightarrow x = 3$ or $\displaystyle x = -1$

    let $\displaystyle m_1$ be the slope of the tangent line that intersects with $\displaystyle y = x^2$ at $\displaystyle x = 3$. thus $\displaystyle m_1 = 2x = 2(3) = 6$

    so the first tangent line is: $\displaystyle \boxed {y = 6x - 9}$

    in a similar fashion, we can find the tangent line that intersects with $\displaystyle y = x^2$ at $\displaystyle x = -1$ to be $\displaystyle \boxed {y = -2x - 1}$


    The last question i have is how you guys put square roots and other symbols in. Can't seem to find them. Thanks a lot.
    Use LaTex or if you don't want to, type sqrt(x) to mean $\displaystyle \sqrt {x}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Apr 22nd 2011, 02:37 AM
  2. Replies: 0
    Last Post: Jan 24th 2011, 11:40 AM
  3. Replies: 2
    Last Post: Nov 6th 2009, 02:51 PM
  4. Replies: 1
    Last Post: Jan 7th 2009, 01:59 PM
  5. Fréchet derivative and Gâteaux derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 23rd 2008, 04:40 PM

Search Tags


/mathhelpforum @mathhelpforum