Question

if f(2)=3 and f'(2)=5 find and equation of the tangent line and the normal line to the graph of y=f(x)
I know satellite73 answered this, but I am curious what the normal line's equation is and how to find it

Answer 1

Normal line is the line perpendicular to the tangent line and goes through the point at (2,3).

Answer 2

Or whatever point of tangency we are talking about (2,3) being the one here.

Answer 3

Okay, so the inverse of the tangent line: y=5x-7

Answer 4

What's the easiest way to find the inverse?

Answer 5

You want to find the inverse now?

Answer 6

Yeah because I already have found the tangent line.

Answer 7

Since lines are 1 to 1, all you need to do is solve for x.
Replace x with f^(-1)(x) and y with x.

I think you are confused.

Why are we finding the inverse of the line?

Answer 8

Sorry, I thought that was just another name for the normal line... >.<

Answer 9

Nope :p

Answer 10

So after we find the slope of the tangent line.
Let's call that slope m.
Then the slope of the normal line with be -1/m.

Answer 11

Lines have form y=slope*x+b

Answer 12

The slope of the normal line is -1/m
So we have y=-1/m*x+b

Answer 13

So it's just -1/5x-7?

Answer 14

Did you put your point into find the y-intercept?

Answer 15

o.o

Answer 16

y=-1/m*x+b
The point this lines goes through or should go through is (2,3)

put that point in

3=-1/m*2+b
solve for b.

3=-2/m+b

3+2/m=b

So you have
y=-1/m*x+(3+2/m)

Answer 17

So, y=-1/5x+17/5 ?

Answer 18

yep

Answer 19

Cool ^w^ Thank you!