find an equation of the normal line to the curve

paralell to

i cant seem to find the slope of the normal line

im confused

:(

answer at the back of book :

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- Dec 17th 2006, 06:04 AM^_^Engineer_Adam^_^Derivative and normal
find an equation of the normal line to the curve

paralell to

i cant seem to find the slope of the normal line

im confused

:(

answer at the back of book : - Dec 17th 2006, 06:23 AMThePerfectHacker
You have,

Thus,

You can write,

Slope is 1, Intercept is 0.

Thus, you need to find the point(s) where the derivative (slope) of the normal line is -1. The reason why -1 is because if the derivative is**tangent**to the curve, but you need the**normal**line. Which is found by taking the reciprocal of the slope and making it change signs. In this case one.

Thus, find all such that,

Where,

- Dec 17th 2006, 06:33 AMearboth
Hello,

two lines are perpendicular if the product of their slopes equals -1.

. k_1 is the y-intercept of the line l_1

. k_2 is the y-intercept of the line l_2

With your problem: l_1 : y = x, that means the slope m_1 = 1

thus the perpendicular line l_2 has the slope m_2 = -1

Now find the gradient of your function which has the same value as the slope of the perpendicular line:

. y' = -1. Solve for x. You'll get x = 1.5.

Plug in this value into the equation of your function to calculate the y-value: y = 1.25. Now you have a point (1.5, 1.25) and the slope (-1). Use the point-slope-formula to get the equation of the line:

I've attached a sketch of your function and the two lines.

EB - Dec 17th 2006, 06:50 AMSoroban
Hello, ^_^Engineer_Adam^_^!

I don't agree with their answer . . . Is there a typo?

Quote:

Find an equation of the normal line to the curve parallel to

The line has slope

. . Our normal will also have slope

A normal to a curve is perpendicular to the tangent at that point.

. . Hence, the tangent will have slope

The slope of a tangent is given by the derivative: .

The tangent has slope when: .

. . and: .

The normal contains the point and has slope .

Its equation is: .

- Dec 17th 2006, 11:54 AManthmoo
I agree with Soroban on this one. However, I think there is a conflict between the answer that Soroban got and the answer in the back of the book.

Soroban got:

Back of book:

I started doing the working on paper for this one but I made a mistake :( on one part of the working after finding the coordinates of intercept! That's why I didn't post....

Following the working of Soroban, I would say it is the back of the book that is incorrect!