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Math Help - Which of the following is larger?

  1. #1
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    Which of the following is larger?

    Suppose f has a continuous positive second derivative for all x. Which of the following is larger?
    f(1 + deltax)
    f(1) + f '(1)*deltax

    I need an explanation, my first instinct is to think that it is the first choice because of the positive second derivative.
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  2. #2
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    Quote Originally Posted by Latszer View Post
    Suppose f has a continuous positive second derivative for all x. Which of the following is larger?
    f(1 + deltax)
    f(1) + f '(1)*deltax

    I need an explanation, my first instinct is to think that it is the first choice because of the positive second derivative.
    f(1) + f'(1)(\Delta x) is a tangent line approximation of f(1 + \Delta x)

    f(x) is concave up ... a tangent line approximation of f(1 + \Delta x) would be less than the actual value of f(1 + \Delta x) because the tangent line lies beneath the curve.
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