Question

Application of differentiation.
Find the equation of the normal to the curve y=(x+2)e^x-3x at the point (0,2).

Answer 1

dy/dx at (0,2) = 0
i don't know what to do next.

Answer 2

@ startanewww what did you get on your derivative at (0,2)?

Answer 3

isn't it 0?

Answer 4

after getting the slope at (0,2) find the normal means perpendicular to the line at (0,2)

Answer 5

1st find the equation of tangent to the curve...

Answer 6

slope perpendicular to it is m2= - 1/m1

Answer 7

y-y1 = m(x-x1)

Answer 8

but the slope I found for dy/dx at (0,2) is zero. What can i do?

Answer 9

then, the slope of the normal will be -1/0 = infinity
how can i find the equation of normal?

Answer 10

Diffrentiate y=(x+2)e^x-3x

Answer 11

u know Product Rule ?

Answer 12

u get slope = -1

Answer 13

SO...Slope of Normal = -1 / m1 = -1/-1 = 1

Answer 14

Nw just write the equation using points (0,2) m = 1

y-y1 = m(x-x1)

Answer 15

y'=e^x+(x+2)e^x-3
dy/dx at (0,2) = e^0 + (0+2)e^0 - 3 = 0

Answer 16

am i correct?

Answer 17

y=(x+2)e^x-3x

y' = (x+2) *1 + e^x *1 - 3

Answer 18

differentiating e^x gives e^x right?

Answer 19

am i correct?

Answer 20

lets say y'=0, can you form a line perpendicular to the curve? try it :D

Answer 21

first fint an equation of the line tangent to the curve at (0,2)

Answer 22

(y-2)/(x-0)=0
y=2?

Answer 23

what about the equation of normal?

Answer 24

yes correct :D then ?

Answer 25

what can i do?

Answer 26

the slope will be infinity....

Answer 27

what is a line perpendicular to line y=2?

Answer 28

at (0,2) ?

Answer 29

will the slope of the normal be infinity ?

Answer 30

but -1/0 = infinity?

Answer 31

x=0 is the line

Answer 32

i don't know the answer....

Answer 33

i think you are right

Answer 34

ah ok theres no answer in the book? :D

Answer 35

my classmates said the answer was x=0

Answer 36

hmm the line perpendicular to y=2 is the y axis or the vertical line

Answer 37

ok so the answer should be x=0 only?

Answer 38

hmm it can be x=0

Answer 39

x = 0 to infinity?

Answer 40

it could be y= 0 to 2, or 2 to infinity, or y= 0 to negative infinity

Answer 41

?????? how come

Answer 42

equation of the normal at (0,2)...? should there be only one answer?

Answer 43

because line tangent to the curve is y=2 or the horizontal line, now the line normal to it is the line perpendicular to y=2,, w/c are ________ ?

Answer 44

vertical lines

Answer 45

?

Answer 46

the vertical line y axis

Answer 47

yess correct :D

Answer 48

so what is the final answer? x=0 ?