maths help pls (1 Viewer)

[scarvesss]

the line y=mx is a tangent to the curve y=e^(3x). find m

 

[scarvesss]

pls

 

[Mr Slick]

differentiate y=e^(3x) . WHatever you get, put m= that answer

 

[Mr Slick]

so that is m=3e^3x

 

[scarvesss]

the answer is apparently 3e. i would usually think to do the same thing but considering its a question 10 in trial hsc i think there is somewhere where we are going wrong

 

[Mr Slick]

their answer is wrong

the answer is apparently 3e. i would usually think to do the same thing but considering its a question 10 in trial hsc i think there is somewhere where we are going wrong

 

[scarvesss]

ill take your word for it

 

[RealiseNothing]

the answer is apparently 3e. i would usually think to do the same thing but considering its a question 10 in trial hsc i think there is somewhere where we are going wrong

3e can't be right, because that's a constant gradient, and hence that would mean is a linear function, which we know it's not.

 

[fortune_cookie]

To be a tangent it must have a common point and the same gradient at that point

So

mx = e^(3x) ---- eqn 1 (Equating y values)

m= 3e^(3x) --- eqn 2 (Equating gradients)

Divide eqn 2 by eqn 1 (note we can do this as e^(3x) is never zero)

m/(mx) = [3e^(3x) /e^(3x) ]

1/x = 3

x=1/3


Now sub back into eqn 2

m= 3e^( 3*(1/3))

m=3e

 

[nightweaver066]

3e can't be right, because that's a constant gradient, and hence that would mean is a linear function, which we know it's not.

It doesn't mean that e^3x has to be a linear function.. The line is just a tangent and 3e is correct.

 

[scarvesss]

holy shit fortune_cookie* you killed it. never would have thought to do that. and im glad others didnt as well

 

[RealiseNothing]

It doesn't mean that e^3x has to be a linear function.. The line is just a tangent and 3e is correct.

I realise now lol..... was thinking of something completely irrelevant.

 

[Drongoski]

m = 3e is correct.

If you think of it: y = e^3x is y = (e³)^x is just anothe exponential function roughly y = 20.0855^x

Its graph looks like the typical one for, say, y = 2^x crossing the y-axis at 1. y = mx is just a straight line thru the origin. Only one such straight line (i.e. for only one value of m) can touch the graph of y = e^3x and that occurs at where x = 1/3 for m = 3e as ably worked out by Mr fortune-cookie.

Edit

Some of you more able than I can show the graphs of the exponential function and the tangent line y = mx.

 

[qwerty44]