derivative satisfying a quadratic equation

[canterbury1176]

Hi all,

Needing a point in the right direction here as I don't really know where to start and have been stuck for days. I have figured out question e but have included it as question f requires it for context. Do I set the derivative above to =0, then rearrange to get the quadratic they've given me below? If so I can't figure out how to do this.

Thanks,
canterbuty1176

 

[Deleted member 4993]

Hi all,

Needing a point in the right direction here as I don't really know where to start and have been stuck for days. I have figured out question e but have included it as question f requires it for context. Do I set the derivative above to =0, then rearrange to get the quadratic they've given me below? If so I can't figure out how to do this.

Thanks,
canterbuty1176

Have you tried to get rid of the sq-rt. part (by squaring T'(z), etc.)? What did you get in part (c) that is used in the hint?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[canterbury1176]

Hi Subhotosh Khan and thanks for the response,

I haven't really tried anything that isn't nonsense yet as I don't understand what the question is asking. The answers to part c were values of x from a quadratic and were x= 8k/13, 8k/3. Was I correct in saying that I am supposed to set T'(z) to 0 and rearrange?
Thanks

 

[Deleted member 4993]

Hi Subhotosh Khan and thanks for the response,

I haven't really tried anything that isn't nonsense yet as I don't understand what the question is asking. The answers to part c were values of x from a quadratic and were x= 8k/13, 8k/3. Was I correct in saying that I am supposed to set T'(z) to 0 and rearrange?
Thanks

Yes.

Have you tried to get rid of the sq-rt. part (by squaring T'(z) = 0, etc.)?

 

[canterbury1176]

As for getting rid of the square roots I'm not sure what you mean by squaring T'(z)=0, do you mean squaring the entirety of both sides of the equation? Wouldn't the square roots in the derivative cancel out because everything that is in them is squared? Like as attached? ->
Also, before trying to rearrange the equation, should I substitute the values from part C in or try to rearrange it as it is in the picture attached?
Thanks

 

[Steven G]

The name of the function, T', just happens to be the derivative of some function. You should just think of T'(z) as some function. This problem has nothing at all to do with derivatives.

The problem says that if T'(z) = 0 then 39z^2 - 128Dz + 64 D^2 = 0.

I would start to find the z-value which makes T'=0 and eventually you will find out the T'=0 only when 39z^2 - 128Dz + 64 D^2 = 0

For example, SUPPOSE T'(z) simplifies to (z^2 + 11)(3z^2 +12)(9z^2 - 128Dz + 64 D^2)/( basically anything) then T'=0 only if 9z^2 - 128Dz + 64 D^2 = 0 which is what you want!

 

[Dr.Peterson]

As for getting rid of the square roots I'm not sure what you mean by squaring T'(z)=0, do you mean squaring the entirety of both sides of the equation? Wouldn't the square roots in the derivative cancel out because everything that is in them is squared? Like as attached? ->
Also, before trying to rearrange the equation, should I substitute the values from part C in or try to rearrange it as it is in the picture attached?
Thanks

The suggestion about squaring means that if you set T'(z) equal to 0, then move one term to the right side so you have two equal fractions, you can either "cross multiply" or just multiply both sides by both denominators to clear fractions. Then square both sides, which will eliminate the radicals. Then you can continue rearranging.

But in your work, you have a major error: [MATH]\sqrt{80^2 + z^2}\ne 80 + z[/MATH]! You must learn well that it is not true that [MATH]\sqrt{a^2 + b^2}= a + b[/MATH]; in fact, [MATH](a+b)^2 = a^2 + 2ab + b^2[/MATH], not [MATH]a^2 + b^2[/MATH].

If you want to prove something is true for all z, it is useless to replace z with specific values. They are telling you to replace variables with variables, not with numerical values.