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Math Help - Finding Differentiable Values

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    Finding Differentiable Values

    Find all values of x for which the function y=(the square root of x)/(5x-2) is differentiable.
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  2. #2
    Junior Member star_tenshi's Avatar
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    Quote Originally Posted by CalcQueen View Post
    Find all values of x for which the function y=(the square root of x)/(5x-2) is differentiable.
    In order for y to be differentiable, then y and y' must be defined, or real.
    For y, the numerator confines anything inside the squareroot to be greater than or equal to zero: x \geq 0.
    When the denominator equals to zero, we know the function becomes undefined. This occurs when 5x-2 = 0 \Rightarrow x = \frac{2}{5}
    Thus our conditions are: x \geq 0, x not equal to \frac{2}{5}

    Upon differentiating to y', we can see that the same conditions for x are required for y' to be defined.
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