Question

Find the equation for the normal line to f at the point (-2, f(-2)).
f(x) = 3x- x^2

Answer 1

normal line means that it is perpendicular

Answer 2

so what is the (-2, f(-2) for

Answer 3

i know normal means perpendicular. idk how to get he equation

Answer 4

sub x=-2 into the f(x) equation to give you the y value they want you to use.
Take the derivative of f(x) to get the slope.
Use that slope and that point to find the normal line.

Answer 5

perp slope are flip and negate

Answer 6

for teh der, i got f' is 3x - 2x....wat is teh der..i think its wrong

Answer 7

f'=[3x- x^2]'
=3- 2x

Answer 8

this tells us the slope of the tangent at any point

Answer 9

-1/f' = slope of the normal at any given point then

Answer 10

so do i pug in -2 to get teh der now ...is it 7

Answer 11

since it wants the normal at -2, then yes; use -2

Answer 12

so we use this slope of "1" in our equation for the line; do you recall the point slope equation for a line?

Answer 13

wait so the slope is 7 but its supposed to be neg. reciprocl so shudnt it be 1/7 te hslope

Answer 14

the slope aint 7, its -1

Answer 15

your right... 7 is good, I was solving some make believe problem in my head lol

Answer 16

-1/7 is the normal slope yes, well stick with that :)

Answer 17

my final equation is y +10 = -1/7 x +2/7...is taht correct

Answer 18

I stand corrected; for the normal slope use the opposite reciprocal.

Answer 19

maybe, lets see if i can stick with it :)

y = (-1/7)x +(1(-2)/7) + f(-2)

y = (-1/7)x -2/7 -10(7)/7

y = (-1/7)x +(-2-70)/7

y = (-1/7)x -72/7

might be good

Answer 20

y = m(x-Px)+Py

y = mx-mPx+Py

Answer 21

http://www.wolframalpha.com/input/?i=plot+y+%3D+%28-1%2F7%29x-70%2F7+and+y%3D3x-x^2+and+y%3D7x%2B4%2C+x%3D-5+to+5%2Cy%3D-12+to+-8

Answer 22

thank u very much :)