Difficult graph sketching helpz needed (1 Viewer)

blackops23 · Sep 27, 2011

Sketch: $x = \frac{-4}{3}e^{3-3t} - 2t + \frac{10}{3}$

Sorry I've no idea what to do with this question, what are some starting steps I can employ to determine the shape of the graph and then sketch it?

Thank you, appreciate the help

taeyang · Sep 27, 2011

$\text{This is pretty weird but here goes}\\\\ x = \frac{-4e^{3-3t}}{3}-2t-\frac{10}{3}\\\\ $Firstly, I like to find the first derivative, for the stationary points$\\ $so now you should end up with..$\\\\ dx/dt = 4e^{3-3t}-2\\\\ $stationary point when derivative = 0$\\\\ \therefore 2 = 4e^{3-3t}\\\\ \therefore ln(0.5)= 3-3t\\\\ \therefore t = \frac{ln(0.5)-3}{-3}\\\\ $Now just simply check with the second derivative whether it is a maximum or minimum point\\\\ d^{2}x/dt^{2} = -12e^{3-3t}\\\\ \therefore $When$ t = {ln(0.5)-3}/{-3}\\\\ The point should end out to be a maximum, so now you've found that, you can just find any points of intersection (to be completely honest, I didn't know how to find them for the$

"t" axis, but the x axis should be x = -23.45 when t = 0) So now all I did was set up a table of values for t = -1000 -100 - 10 -1 0 1 10 100 1000... And found what happens to the curve when t approaches infinity and minus infinity, good luck!

Sorry about the horrendous looking graph..... ^.^ just whipped it up. By the way the graph should be a smooth curve to the left of t = 1.23 if you know what I mean

Difficult graph sketching helpz needed (1 Viewer)

blackops23

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taeyang

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