consider the two functions:
f(x, a) =70- 5xa & g(x) = 30 +4x
a) find the x value of the point where the two equations intersect (in terms of the variable a)
b) find the value of the functions at the point where the two equations intersect (in terms of the variable a).
c) take the partial derivate of f with respect to x, \partial f / \partial x, and with respect to a, \partial f / \partial a
d) what are the values of these derivatives , when x= 3 and a=2, which can be written as \partialf /\partialx (3,2) and \partial f /\partiala (3,2)
e) next caculate these two numbers:
\upsilon1 = (\partialf /\partialx ( 3,2)) 3 / f (3,2)
\upsilon2 = (\partialf /\partiala ( 3,2)) 2 / f (3,2)
f) finally write out these equations in term of a and x and simplify,
\upsilon1 = (\partialf /\partialx ( x, a)) x / f (x, a)
\upsilon2 = (\partialf /\partialx ( x, a)) a / f (x, a)