Question

The Slope of the line normal to the curve e^x- x^3+ y^2= 10 at the point (0, 3) is

Answer 1

First use implicit differentiation to calculate an expression for the slope at any point (x,y)

Answer 2

@asnaseer I got (y'=-e^x+ 3x^2)/2y

Answer 3

that is correct.
Now use this to calculate the slope to the curve at the point (0, 3)
Finally use the fact that the product of the slopes of to lines that are perpendicular to each other is -1 to work out the slope of the normal

Answer 4

so @asnaseer would I plug in (0, 3)... (y' -e^0 + 3*0^2)/ 2*3 ?

Answer 5

yes, assuming you meant y'=(-e^0+3*0^2)/2*3

Answer 6

yes

Answer 7

then you're good to go :)

Answer 8

@asnaseer the answer seems to be -1/6 did I do it correctly?

Answer 9

or -x/6

Answer 10

yes - that is the slope to the curve at (0, 3)

now you just need to calculate the slope of the normal line using the technique I mentioned above :)

Answer 11

how can it be -x/6?

Answer 12

I don't know that's what the calculator said but I change it to -1/6

Answer 13

there is no 'x' in the expression

(-e^0+3*0^2)/2*3

Answer 14

and, you don't need a calculator for this

Answer 15

I do, How do I do what you said above?

Answer 16

take each term:

what is e^0=?

Answer 17

1?

Answer 18

correct (because any number to the power of zero is one)

next what is:

3*0^2 = ?

Answer 19

0

Answer 20

correct (because anything times zero is zero)

finally, what is:

2*3 = ?

Answer 21

8

Answer 22

are you sure?

Answer 23

Oh sorry I read it as 2^3 that would be 6

Answer 24

good, so we end up with:

y' = (-e^0+3*0^2)/2*3 = (-1 + 0)/6 = -1/6

no calculator required :)

Answer 25

Oh yeah your right :) guess I'm getting to use to a calculator. There is another part to do?

Answer 26

this just gives you the slope to the curve at the point (0,3)
you are asked to find the slope of the NORMAL - i.e. the slope of the line that would be perpendicular to this line

Answer 27

okay so in my head I would take it back to algebra and tell myself to find the negative reciprocal, but this is calc so I have to do something else don't I?

Answer 28

no - don't try to complicate things just because you are in calc :)

your 1st instinct is correct :)

Answer 29

Oh gees easiest thing I've done all day god I miss algebra. So the final answer would be 6

Answer 30

the "calc" part was used to calculate the initial expression for the slope at any point

Answer 31

perfect! :)

Answer 32

Thank you one billion times

Answer 33

you are more than welcome my friend :)