Question

Post #2

Answer 1

@sirm3d

Answer 2

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Answer 3

it is correct ..but dont understand it..cuz i copied the solution LOL

Answer 4

actually i do understand, but cant do it alone..like what steps to take, what to isolate, what to combine

Answer 5

when you make a frontal view the cylinder inside a sphere, you'' see a rectangle inside a circle.

Answer 6

To maximize the volume of the cylinder V =pi R^2 h, we need to take the derivative of the volume function (to maximize is equivalent to taking the derivative).
But we only know how to take the derivative of V(R) or V(h), NOT V(R, h).
So we need to write V as a function of either R or h, not both. which means we need two write an equation converting R to h, or h to R, using a right triangle.

Answer 7

r^2 = R^2 + (h/2)^2

Answer 8

Since R^2 is present in the volume function and the triangle equation, we'll write the volume in terms of h.
V= pi (r^2 - h^2/4) h
note that r = radius of the sphere, is constant in this problem.

Answer 9

and we dont need to use the volume of the sphere because we are not optimizing the volume of sphere but the cylinder?

Answer 10

just the cylinder inside the sphere of fixed radius r.

Answer 11

but isnt r and h are both variables

Answer 12

oh nvm

Answer 13

wrong r

Answer 14

r is constant, R is variable

Answer 15

since a volume function v(h) is now determined, different the function, set to zero and solve for the variable h, then R in the triangle equation. finally sub R and h in the volume of the cylinder to get the desired maximum volume.

Answer 16

oh ok got it thx!

Answer 17

and then this one,
when u want to find whether the function is cts, do u just equate them together

Answer 18

equate them at the endpoint x=2.

Answer 19

oh, u sub in x=2 first, and equate them
but isnt that finding intersection point?
so basically u just want to check if x=2 is cts

Answer 20

if the function is continuous at x=2, then the two "curves" have to be connected at x=2.

Answer 21

connected: same x = 2, same y-value.

Answer 22

oh yea