Question

Normal line problem:

Answer 1

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Answer 2

Hello.

Answer 3

First, do you know how to find the equation of a normal line from a point if the function is given?

Answer 4

Find the derivative, plug in x to get the slope and then use that and the given points to find the new equation?

Answer 5

Almost correct.

Answer 6

Do you know that normal line is perpendicular to the tangent line?

Answer 7

Oh, right, negative reciprocal slope.

Answer 8

Yep.

Answer 9

So after we do that how do we know where they intersect? Draw a graph?

Answer 10

First, did you find the equation of the normal line at (5,0) of the function y=25x-5x^2?

Answer 11

Uhm..
\[\ y=25x-5x^2\]
\[\ y'=25-10x~~at~x=5\]
\[\ y'=25-50=-25\]
\[\LARGE y-0=\frac{1}{25}(x-5)\]
\[\LARGE y=\frac{1}{25}x-\frac{1}{5}\]

Answer 12

Good!. Now, let's simplify the problem a bit.
Can you put the equation of the normal line in form of x=ay+b?

Answer 13

Hmm..
\[\LARGE x=-25y+5\]

Answer 14

*25y

Answer 15

Yes. Now, you have to find the intersection between that and y=25x-5x^2.
You can just substitute.

Answer 16

That'll be fun, I think I got it from here, thanks for the help :)

Answer 17

Yep. :)