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

- anonymous

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- anonymous

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

- anonymous

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

- anonymous

isn't it 0?

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## More answers

- anonymous

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

- anonymous

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

- anonymous

slope perpendicular to it is m2= - 1/m1

- anonymous

y-y1 = m(x-x1)

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

u know Product Rule ?

- anonymous

u get slope = -1

- anonymous

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

- anonymous

Nw just write the equation using points (0,2) m = 1
y-y1 = m(x-x1)

- anonymous

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

- anonymous

am i correct?

- anonymous

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

- anonymous

differentiating e^x gives e^x right?

- anonymous

am i correct?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

what about the equation of normal?

- anonymous

yes correct :D then ?

- anonymous

what can i do?

- anonymous

the slope will be infinity....

- anonymous

what is a line perpendicular to line y=2?

- anonymous

at (0,2) ?

- anonymous

will the slope of the normal be infinity ?

- anonymous

|dw:1356675309579:dw|

- anonymous

but -1/0 = infinity?

- anonymous

x=0 is the line

- anonymous

i don't know the answer....

- anonymous

i think you are right

- anonymous

ah ok theres no answer in the book? :D

- anonymous

my classmates said the answer was x=0

- anonymous

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

- anonymous

ok so the answer should be x=0 only?

- anonymous

hmm it can be x=0

- anonymous

x = 0 to infinity?

- anonymous

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

- anonymous

?????? how come

- anonymous

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

- anonymous

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 ________ ?

- anonymous

vertical lines

- anonymous

?

- anonymous

the vertical line y axis

- anonymous

yess correct :D

- anonymous

so what is the final answer? x=0 ?

- anonymous

i would say at point (0,2) it is y= from 0 to 2 vertical line

- anonymous

ok thanks

- anonymous

ok YW,,, good luck now :D

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