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Homework Help: Basic Differentiation

  1. Nov 19, 2007 #1
    [SOLVED] Basic Differentiation

    Hi there, I've heard that this forum is the best for getting some quick help.

    Find the gradient of the tangent to the curve at the given point:
    y = 2x² + 3x + 5 when x = -1

    2. Relevant equations
    Right, I'm very new a this, but dy/dx is the way to go right?

    3. The attempt at a solution:
    y = 2x² + 3x + 5 when x = -1
    dy/dx it, and I get:
    dy/dx=4x + 3
    Substitute -1 in and I get
    y=-1

    So I've now got two points; (-1,-1) but thats not the gradient, but I've got the feeling I'm half way there. Any help would be great thanks!
     
  2. jcsd
  3. Nov 19, 2007 #2

    HallsofIvy

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    Science Advisor

    Well, first of all (-1, -1) is ONE point, not two! But more important, if dy/dx= 4x+ 3, then putting x=-1 gives you dy/dx= -1, not y. At first I thought that it was a typo but then you say "that's not the gradient". It certainly IS the gradient! You are not "half way there", you are completely there!

    (It is true that, if x=-1, y= 2(-1)2+ 3(-1)+ 5= 2- 3+ 5= 4. y= 4 so the graph of the function passes through the point (-1, 4). The tangent line to the curve is y= -1(x+1)+ 4 or y= -x+ 3.)
     
  4. Nov 20, 2007 #3
    Fantastic, I can finish off the rest of the questions now. Thanks!
     
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