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11-26-2012   #1 (permalink)
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Default Calc II question

Find the points on the curve where the tangent line is horizontal or vertical.
x=e^sin(theta), y=e^cos(theta), for 0 less than or equal to x less than 2pi (0<x<2pi)

Answer is vertical (e,1)(1/e,1) horizontal (1,e)(1,1/e)

I need help getting the answer. How do you get those numbers? I need the help by today, the question is due tomorrow.

Last edited by evilxshadow; 11-26-2012 at 05:51 PM.
 
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11-26-2012   #2 (permalink)
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Quote:
Originally Posted by evilxshadow
x=e^sin(x), .
What is this typo supposed to be?

All you need to do is differentiate (you will need the chain rule)
And then solve for when the derivative is either 0 or infinite (may apply if you typo is supposed to say x=e^siny and you decide to rearrange for y)

Stuff to know:
1. The exponential function is always bigger than 0. (For real numbers anyways)
2. Sin(x) only gives values between -1 and 1. When is sinx 0? When is cosx 0?
3. This identity may come in handy sinxcosx=1/2 sin2x; if you have not learnt it yet, I advise you do not use it.

Find these and then carry on with what you do with the more basic derivation questions. [You started with polynomials (x^3+3x^2)... You know how to do these well I assume. Since you are not doing fancy college math I will say that everything they throw at you will have the same technique (only time you need to worry is when you have fractals, |x|, rect(x) and other non differentiable functions, the only one you learn in school is the absolute value, and that one; you know what the minimum is). Same goes for inflection points and such like that. The algebra just becomes nasty.]

And also, since you are doing homework and are not in class, you should consider going to wolframalpha.com and getting it to plot out the graph. Just type plot: exp(sin(x)) ; and it will show you what you are looking at.


If you are still lost post here, or look up a few examples in the textbook.
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Last edited by Nebula; 11-26-2012 at 05:58 PM.
 
11-26-2012   #3 (permalink)
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Quote:
Originally Posted by Nebula
What is this typo supposed to be?

All you need to do is differentiate (you will need the chain rule)
And then solve for when the derivative is either 0 or infinite (may apply if you typo is supposed to say x=e^siny and you decide to rearrange for y)

Stuff to know:
1. The exponential function is always bigger than 0. (For real numbers anyways)
2. Sin(x) only gives values between -1 and 1. When is sinx 0? When is cosx 0?
3. This identity may come in handy sinxcosx=1/2 sin2x; if you have not learnt it yet, I advise you do not use it.

Find these and then carry on with what you do with the more basic derivation questions. [You started with polynomials (x^3+3x^2)... You know how to do these well I assume. Since you are not doing fancy college math I will say that everything they throw at you will have the same technique (only time you need to worry is when you have fractals, |x|, rect(x) and other non differentiable functions, the only one you learn in school is the absolute value, and that one; you know what the minimum is). Same goes for inflection points and such like that. The algebra just becomes nasty.]

And also, since you are doing homework and are not in class, you should consider going to wolframalpha.com and getting it to plot out the graph. Just type plot: exp(sin(x)) ; and it will show you what you are looking at.


If you are still lost post here, or look up a few examples in the textbook.
also its supposed to be theta, not x
for the stuff to know part, wouldnt it be "when is sinx =1"? because isnt it e^sin(x) = 0?

Last edited by evilxshadow; 11-26-2012 at 06:08 PM.
 
11-26-2012   #4 (permalink)
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No, it is 0, when you do the differentiation you should see.
Let y=e^u(x)
By the chainrule you get
y'=u'(x)u(x)e^u(x)

Since exponents are never 0, you have to look at the u(x) and u'(x) parts.
Ask yourself 'how can I make these 0?'
There will be several instances.

I shall stress the point with exponentials never being zero (or negative)...
e^sin(x) will never ever be equal to 0.
However its derivative will have points that are 0 and negative.
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Last edited by Nebula; 11-26-2012 at 06:14 PM.
 
11-26-2012   #5 (permalink)
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i see it now, thanks alot
 

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