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

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

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

[0, 49]

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

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

Can you finish?

3. 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?

4. 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).