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Math Help - Find the number c that satisfies the conclusion of Rolle's Theorem.

  1. #1
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    Find the number c that satisfies the conclusion of Rolle's Theorem.

    f(x) = squaroot(x) -(1/7)x

    [0, 49]
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  2. #2
    Senior Member eumyang's Avatar
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    f(x) = \sqrt{x} - \frac{1}{7}x

    Find the derivative of f(x) and set equal to 0:
    \begin{aligned}<br />
f(x) &= x^{1/2} - \frac{1}{7}x \\<br />
f'(x) &= \frac{1}{2}x^{-1/2} - \frac{1}{7} \\<br />
0 &= \frac{1}{2 \sqrt{x}} - \frac{1}{7} \\<br />
\end{aligned}

    Can you finish?
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  3. #3
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    1/2(sqaroot(x)) = 1/7
    move -1/7 to other side of equal side
    cross multiply to solve for x

    49/4
    thank you
    Also, how do I write out the equation like you did? For example, instead of using squarootx i can write out the actual square root symbol?
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  4. #4
    Senior Member eumyang's Avatar
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    Learn LaTeX. While you're in the editing window, at the end of the 2nd row of formatting/functions (the one that starts with bold, italics, underline), you'll see the TeX button. Click it, and the math tags appear:

    [ MATH ][ /MATH ]

    (I added extra spaces so that the tags would appear.) You'll have to learn the syntax to type the equations in. Look at the LaTeX Help subforum. Here's what I typed so that the original equation would appear:
    [ MATH ]f(x) = \sqrt{x} - \frac{1}{7}x[ /MATH ]
    f(x) = \sqrt{x} - \frac{1}{7}x
    (again, without the extra spaces).
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