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Math Help - Differentiation Problem

  1. #1
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    Differentiation Problem

    Can anyone help me out with this one problem please, didn't really learn this type of problem yet.

    find a and b such that f is differentiable everywhere

    f(x)= ax^3, x=less than or equal to 2
    x^2+b, x=greater than 2

    thanks
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  2. #2
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    Quote Originally Posted by soldatik21 View Post
    Can anyone help me out with this one problem please, didn't really learn this type of problem yet.

    find a and b such that f is differentiable everywhere

    f(x)= ax^3, x=less than or equal to 2
    x^2+b, x=greater than 2

    thanks
    Hint: If f(x) is differentiable everywhere, then it is continuous and smooth at all points.

    Here, the only possible point of discontinuity is at x = 2.

    So you need to find an a and b so that the function is the same at that point.

    Have a go.
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  3. #3
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    i understand that part that at x=2 the two functions have to be equal. but doesn't that give you more than one answer for example a can be 2 and can be 12? or a can be 1 and b can be 4?
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