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  1. #1
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    Exclamation ap calc

    for what values of a and c is the function differentiable at x=2?

    f(x)= x+c, x>2
    ax^2, x<(or equal to) 2

    how do i start this problem? thanks so much
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  2. #2
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    Quote Originally Posted by holly123 View Post
    for what values of a and c is the function differentiable at x=2?

    f(x)= x+c, x>2
    ax^2, x<(or equal to) 2

    how do i start this problem? thanks so much
    Well, first it must be continuous so 4a = c+2. Next, the left and right derivative must equal so 4a = 1. Two equation and two unknowns.
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    Quote Originally Posted by holly123 View Post
    for what values of a and c is the function differentiable at x=2?

    f(x)= x+c, x>2
    ax^2, x<(or equal to) 2

    how do i start this problem? thanks so much
    if the function is differentiable, then it has to be continuous ...

    \lim_{x \to 2^+} f(x) = \lim_{x \to 2^-} f(x)

    2+c = 4a


    also, since f(x) is differentiable at x = 2 ...

    \lim_{x \to 2^+} f'(x) = \lim_{x \to 2^-} f'(x)

    1 = 4a

    solve for a and c.
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