How many critical points ought function have

Reference no: EM13968036

Suppose the line L1 is parametrized by r1(t) = <2t+5,3t,t-3>, and the line L2 is parametrized by r2(t)=<t+1,3-2t,-2>.?

Define the function f(s,t) to be the square of the distance between r1(t) and rs(s)

a) Think about what happens to f(s,t) as s,t->+-infinity. How many critical points ought f have.

b) write the formula for f(s,t) and all its critical points . Identify f as one of the "quadratic surfaces"

c) Find s* and t* so that the distance between r1(t*) and r2(s*) is as small as possible. the line segment between these points has an interesting geometric property related to L1 and L2. What is the property?

Reference no: EM13968036

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