What function to use and how to use it
1 answer:
That's the wrong right triangle to draw. Reading the problem carefully we want this one, figure attached.
So we have the usual 30/60/90 triangle but not to scale. The sides come in ratio 1:√3:2=x:100:hypotenuse. So
x = 100/√3 ≈ 57.735
We add that to our 133.2 for the total height of the Cyclone, 190.935.
Answer: 190.9
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Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
Taken together, we find that (0, 0, 0) appears to be the only critical point on
within the ball. At this point, we have 
.
Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian
with partial derivatives (set to 0)
We then observe that
So, ignoring the critical point we've already found at (0, 0, 0),
So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of
, at which points we get a value of either of 
, with the maximum being the positive value and the minimum being the negative one.
Taken together, we find that (0, 0, 0) appears to be the only critical point on
Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian
with partial derivatives (set to 0)
We then observe that
So, ignoring the critical point we've already found at (0, 0, 0),
So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of