Results 1 to 3 of 3

Thread: finding the equation of a tangent line

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    42

    Exclamation finding the equation of a tangent line

    help please and thank you!!


    y=e^x

    find the equation of the tangent line at x=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by cottekr View Post
    help please and thank you!!


    y=e^x

    find the equation of the tangent line at x=0
    A tangent line is a straight line, so is of the form

    $\displaystyle y=mx+c$ where m is the gradient and c is the y-intercept.

    To find the gradient of this tangent, we need to differentiate the function and evaluate it at that point.

    $\displaystyle y=e^x$ so $\displaystyle \frac{dy}{dx} = e^x$.

    At the point $\displaystyle x=0$, $\displaystyle \frac{dy}{dx} = e^0 = 1$.

    So the gradient of the tangent at $\displaystyle x=0$ is 1.

    We know that when $\displaystyle x=0, y=1$, so the y-intercept is 1.

    Thus the equation of the tangent is

    $\displaystyle y = x + 1$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2007
    Posts
    127
    Eqn of tangent line: $\displaystyle y-y_1 = m(x-x_1)$ where $\displaystyle m$ is the gradient at the point $\displaystyle (x_1 , y_1)$

    When $\displaystyle x_1=0$, y=$\displaystyle e^0 = 1$

    $\displaystyle \frac{dy}{dx} = e^x $ at $\displaystyle x=0, \frac{dy}{dx} = 1 $

    So the equation of the tangent line is

    $\displaystyle y-1 = 1(x-0)$

    $\displaystyle y=x+1$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: Jan 12th 2011, 02:38 PM
  2. Replies: 2
    Last Post: Oct 12th 2010, 02:24 PM
  3. finding equation of a tangent line
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 10th 2009, 06:55 PM
  4. Finding equation of a Tangent Line
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jun 2nd 2009, 02:47 PM
  5. Finding equation of a tangent line.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 5th 2008, 07:20 PM

Search Tags


/mathhelpforum @mathhelpforum