# Stationary Points

• February 18th 2008, 04:06 AM
richard_c
Stationary Points
If the value of a variable ‘R’ is related to the value of a variable ‘t’ by the following:

R=0.25t^2 + 4t

And I want to find the value of ‘t’ that produces a stationary value for the variable ‘R’ -how would I go about this?

Also, how would I go about finding the value of Q at this stationary point?
• February 18th 2008, 05:49 AM
TriKri
Quote:

Originally Posted by richard_c
If the value of a variable ‘R’ is related to the value of a variable ‘t’ by the following:

R=0.25t^2 + 4t

And I want to find the value of ‘t’ that produces a stationary value for the variable ‘R’ -how would I go about this?

A stationary point has a slope of zero, so in your case $\frac{dR}{dt} = 0.25\cdot 2t + 4 = 0\ \Leftrightarrow\ t/2 = -4 \ \Leftrightarrow\ t = -8$

Quote:

Also, how would I go about finding the value of Q at this stationary point?
You haven't defined Q?
• February 18th 2008, 12:33 PM
richard_c
Forgive me for prehaps asking a daft question, but what happens to the 0.25? or does this get disregarded?

Thanks
• February 18th 2008, 12:37 PM
richard_c
Sorry - the second part was meant to read - -

"Also, how would I go about finding the value of Q at this stationary point?"
• February 18th 2008, 04:01 PM
TriKri
Quote:

Originally Posted by richard_c
Forgive me for prehaps asking a daft question, but what happens to the 0.25? or does this get disregarded?

Do you mean while deriving? I don't understand the question, I have taken it into account as you can see...

Quote:

Originally Posted by richard_c
Sorry - the second part was meant to read - -

"Also, how would I go about finding the value of Q at this stationary point?"

Isn't that what you wrote before too? Still, what is Q?
• February 19th 2008, 04:43 AM
richard_c
Sorry - the second part was meant to read - -

"Also, how would I go about finding the value of R at this stationary point?"
• February 19th 2008, 08:37 AM
TriKri
Well, you now know the valu for t, right? Just go ahead insert it into the expression for R, and you should be able to calculate the value of the expression which also will give you the value of R.