# Point on a Curve parallel to a line [Something Missing ?]

• Nov 7th 2009, 02:28 PM
StarlitxSunshine
Point on a Curve parallel to a line [Something Missing ?]
This is a question from a worksheet my teacher printed out of a book. It seems like something is missing because I don't know what to do with the question...

The point on the curve $\displaystyle y = \sqrt[2]{4x+2}$ at which the normal is parallel to the line $\displaystyle y=-x+8$ is

1. (A) $\displaystyle (\frac{1}{4}, \sqrt[2]{2})$
2. (B)$\displaystyle (\frac{-1}{2}, 0)$
3. (C)$\displaystyle (0, \sqrt[2]{2})$
4. (D)$\displaystyle (\frac{1}{2}, 2)$
5. (E)$\displaystyle (1, \sqrt[2]{6})$
• Nov 7th 2009, 02:34 PM
tonio
Quote:

Originally Posted by StarlitxSunshine
This is a question from a worksheet my teacher printed out of a book. It seems like something is missing because I don't know what to do with the question...

The point on the curve $\displaystyle y = \sqrt[2]{4x+2}$ at which the normal is parallel to the line $\displaystyle y=-x+8$ is

1. (A) $\displaystyle (\frac{1}{4}, \sqrt[2]{2})$
2. (B)$\displaystyle (\frac{-1}{2}, 0)$
3. (C)$\displaystyle (0, \sqrt[2]{2})$
4. (D)$\displaystyle (\frac{1}{2}, 2)$
5. (E)$\displaystyle (1, \sqrt[2]{6})$

Nothing's missing: the normal to a point on the graph of a function is a straightline through that point which perpendicular to the tangent to the function on that point, so you must:

2) find what the slope of a NORMAL to any point of the graph is

3) make this slope equal to the given line's slope (so that they'll be parallel)

4) solve and find out what x is, and then substitute in the function and find out what the y-coordinate is.

Tonio
• Nov 7th 2009, 02:52 PM
StarlitxSunshine
Quote:

Originally Posted by tonio
Nothing's missing: the normal to a point on the graph of a function is a straightline through that point which perpendicular to the tangent to the function on that point, so you must:

2) find what the slope of a NORMAL to any point of the graph is

3) make this slope equal to the given line's slope (so that they'll be parallel)

4) solve and find out what x is, and then substitute in the function and find out what the y-coordinate is.

1). The derivative is $\displaystyle \frac{2}{\sqrt[2]{4x+2}}$