3Dplot in maple

Question

Hello all,

I am considering the function $f(t,u)=e^{(t^{2}+10u-1)}$.

I am also considering the tangent plane $g(t,u)=-121+22t+10u$ at point (11,-12).

I would like to draw a 3Dplot in maple that shows the tangentplane touching the graph of $f(t,u)$ at point (11,-12).

I have typed the following :

plot3d([exp(t^2 + 10u - 1), -121 + 22t + 10*u], t = -1 .. 1, u = -0.7 .. 0.7, color = [red, green])

The 3Dplot is not correct. I have spent much time getting it to work. Could someone please assist me?

Thanks.

Answer 1

plot3d([ exp(t^2 + 10*u - 1), -121 + 22*t + 10*u, [[11,-12,1]] ],
   t = 8 .. 12, u = -15 .. -6, grid=[[151,151],[2,2],[2,2]],
   color = [grey, green, red], style=[patch,patch,point],
   symbol=solidcircle, symbolsize=10, view=-50..50,
   lightmodel=Light2, transparency=[0.1,0.0,0.0]);

Or you could use a narrower pair of ranges for the parameters, eg,

t = 10 .. 12, u = -13 .. -11

That makes it less obvious that the surfaces are not touching along a line. But if you increase the ranges then you can run into rendering issues (with the chopped view, and the large magnitudes).