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

**superduper1** · July 22nd 2010, 10:05 AM

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

[0, 49]

**eumyang** · July 22nd 2010, 10:46 AM

$f(x) = \sqrt{x} - \frac{1}{7}x$

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?

**superduper1** · July 22nd 2010, 05:28 PM

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?

**eumyang** · July 22nd 2010, 07:14 PM

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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