e^x * cos(x) extremums in R

[Toxicone7]

Hello, as the title says I'm asked to find the extremums of this function in R. The first derivative = 0 comes to tanx=-1. My problem is that this has infinite roots

---

and thus, how am I supposed to solve the original problem? I've done this kind of stuff when the function is in [0,π] for example or something defined so the roots of the first derivative are certain.. This is not the case in R.

Thanks in advance,

 

[Deleted member 4993]

Hello, as the title says I'm asked to find the extremums of this function in R. The first derivative = 0 comes to tanx=-1. My problem is that this has infinite roots

---

and thus, how am I supposed to solve the original problem? I've done this kind of stuff when the function is in [0,π] for example or something defined so the roots of the first derivative are certain.. This is not the case in R.

Thanks in advance,

You said:

The first derivative = 0 comes to tanx=-1. ................................... this is incorrect

Please show work.

Use WolframAlfa and plot the function to visually observe the domain and the range of this function.

Then you can justify those mathematically.

 

[Steven G]

Hello, as the title says I'm asked to find the extremums of this function in R. The first derivative = 0 comes to tanx=-1. My problem is that this has infinite roots

---

and thus, how am I supposed to solve the original problem? I've done this kind of stuff when the function is in [0,π] for example or something defined so the roots of the first derivative are certain.. This is not the case in R.

Thanks in advance,

As pointed out already, tan(x)=-1 is not correct. Now just because you get an infinite number of extremums does not necessarily create a problem. Can you nicely describe all of the extremas in one equation or maybe 2 eqs ... or any finite number of eqs?

 

[Toxicone7]

You said:

The first derivative = 0 comes to tanx=-1. ................................... this is incorrect

Please show work.

Use WolframAlfa and plot the function to visually observe the domain and the range of this function.

Then you can justify those mathematically.

Well, take the e^x*sinx, my bad, still same question.

 

[Toxicone7]

As pointed out already, tan(x)=-1 is not correct. Now just because you get an infinite number of extremums does not necessarily create a problem. Can you nicely describe all of the extremas in one equation or maybe 2 eqs ... or any finite number of eqs?

Yeah my mistake about it , but let's take the e^x*sinx, how do we solve that one?

 

[Deleted member 4993]

Yeah my mistake about it , but let's take the e^x*sinx, how do we solve that one?

That is not correct either - it is "more" incorrect than your previous answer. I am afraid that you are not paying attention to the problem.

Please post the EXACT problem as it was presented to you - verbatim.

 

[Steven G]

We solve it by you computing the first derivative and setting it to 0. Then you show us your work at attempting to solve this equation and we will go from there.

 

[Toxicone7]

We solve it by you computing the first derivative and setting it to 0. Then you show us your work at attempting to solve this equation and we will go from there.

Let's start from the beginning. Function is e^x*cosx
I want to find the stationary points of it.
First derivative =0 means cotx=1, which if I remember correctly has infinite roots and therefore there are infinite stationary points? That's what I am trying to get. When I did solve similar problems the function was for example set in [-π,π] or something like it while now, it is set in R.. Thank you

 

[Toxicone7]

That is not correct either - it is "more" incorrect than your previous answer. I am afraid that you are not paying attention to the problem.

Please post the EXACT problem as it was presented to you - verbatim.

Stationary points of e^x*cosx, x in R that's the problem. I don't seem to get how to solve this in R since the first derivative has infinite roots in every period.. I've only solved these in a set domain e.g. [-π,π]. If you could help, that'd be great
Thank you,

 

[Deleted member 4993]

Let's start from the beginning. Function is e^x*cosx
I want to find the stationary points of it.
First derivative =0 means cotx=1, which if I remember correctly has infinite roots and therefore there are infinite stationary points? That's what I am trying to get. When I did solve similar problems the function was for example set in [-π,π] or something like it while now, it is set in R.. Thank you

Please post the EXACT problem as it was presented to you - verbatim.

As you posted the problem - it asks for the value of the function at the extrema - not the x values where extrema occur!

OP read:

"... I'm asked to find the extremums of this function in R"

Looks like you have translated the problem!

 

[pka]

Well, take the e^x*sinx, my bad, still same question.

If \(\displaystyle y=e^x\sin(x)\) then anyone having had basic, basic calculus knows:
\(\displaystyle y'=e^x\sin(x)+e^x\cos(x)\\y''=e^x\sin(x)+e^x\cos(x)+e^x\cos(x)-e^x\sin(x)\)
If you do not then you need to repeat basic calculus and quit wasting time!

 

[Toxicone7]

Please post the EXACT problem as it was presented to you - verbatim.

As you posted the problem - it asks for the value of the function at the extrema - not the x values where extrema occur!

OP read:

"... I'm asked to find the extremums of this function in R"

Looks like you have translated the problem!

Yeah, English isn't my native language and math stuff in it is kinda hard. So, how we do it?

 

[pka]

Yeah, English isn't my native language and math stuff in it is kinda hard. So, how we do it?

Mathematics is not different from language to different language.
You simply seem to not have a basic grasp of calculus in any language.
You need to review basic basic principles of calculus!

 

[Steven G]

I will give you an example. Say we want to know when sin(x)=1. There are infinitely many solutions and they are \(\displaystyle x=\dfrac{\pi}{2} + 2n\pi \: for \: any\: integer\: n\)

 

[HallsofIvy]

I'll try not to be as brutally frank as pka. You are given the function \(\displaystyle y= e^x sin(x)\). Yes, the first thing you want to do is find the derivative of that, using the "product rule". \(\displaystyle y'= e^x cos(x)- e^x sin(x)= 0\). Yes, you can write that as \(\displaystyle e^x cos(x)= e^x sin(x)\) which reduces to \(\displaystyle tan(x)= 1\). Yes, there are an infinite number of solutions to that, because there are an infinite number of local extrema for this function. tan(x)= 1 when \(\displaystyle x= \pi/4\) but also at \(\displaystyle \pi/4\) plus any integer multiple of \(\displaystyle \pi\): \(\displaystyle x= \frac{\pi}{4}+ n\pi\).