Please help me CALC III?

Posted on 2015-10-29 07:28:00 in Math by SELENA

Problem 4 (2 Points):
A mountain rising from a plateau (or flat ground) is modeled as
f(x, y) = {
3(1 ?
?
x
2 + y
2) : ?1 ? x, y ? 1
0 : otherwise
A road up the mountain is modeled as a spiral ?r(t) = at cos(b ln t)?i+atsin(b ln t)?j,
where 0 ? t ?
1
a
. (See Figure 3 on the next page).
(Part a) Find the directional derivative (commonly referred to as grade of
the mountain road) in the direction of the road.
(Part b) What is the directional derivative if a =
1
60 and b =
?
3599 ?

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