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Homework Help: Equation for the line tangent to the graph and use it to approx. f(1.2)

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Write an equation for the line tangent to the graph of f at x = 1 and use it to approximate f(2.1).

    2. Relevant equations

    y = mx+b
    f(1) = 4
    f'(x) = (3x^2 + 1) / 2y
    m = 1/2 when x = 1

    3. The attempt at a solution

    Well, if the line is tangent to the graph of f at x = 1, that means they have the same slope (I think). Thus,

    y = (1/2)x + b​

    I have the point (1, 4) so I plug that in to find b

    4 = (1/2)(1) + b
    b = 8​

    Thus, I have

    y = (1/2)x + 8​

    Since they want me to approximate f(2.1), I would plug in 2.1 for x and solve for y. But, my answer is wrong. The correct answer is

    y - 4 = (1/2)(x-1)
    f(1.2) = 4.1​

    My equation is wrong (and thus my answer), which leads me to believe that I'm approaching this incorrectly.
     
  2. jcsd
  3. May 2, 2010 #2
    4 = (1/2)(1) + b
    b = 8
    ........
    That's wrong. b = 3.5
     
  4. May 2, 2010 #3
    Oh my gosh, I can't believe I did that wrong even after I checked it over a few times!

    Thanks!
     
  5. May 2, 2010 #4
    You wouldn't believe some of the mistakes I've made.
    e.g. In a state competition, I calculated 98 - 64 = 32. We lost by a point.
     
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