Richard
Skinner

rls2723

Sheet #25

Week #4

Problem
3.5.7


http://208.166.239.244/3_5_7.htm

The temperature
in a square plate is given by the equation T = x + 3y. An ant crawled on
the plate along the parabolic path y = x^{2} until it reached the
point (2,4), whereupon it found itself fried. What is wrong with the following
argument?
We can cancel
the two equal terms, concluding that
.
Substituting
the given functions and numbers, we learn that
12 = 0.
Solution:
Some parameters
must be introduced before the chain rule will work.
x = t
y = t^{2}
Now rewrite
the chain rule argument to reflect the new parameters.
All that is
left is substituting in the values and simplifying to find the answer.
= (1)*(1) + (3 * 2t)
=6t + 1