Question

7. Consider the two functions: f(x, a)-40 - 3xa 9(2) 10 + 7x (a) Find the x value of the point where the two equa- (b) Find the value of the functions at the point where erwya tions intersect (in terms of the variable a) the two equations intersect (in terms of the variable a) (c) Take the partial derivate of f with respect to , and with respec t to a. d) What are the values of these derivatives when r - 3 2, which can be written as and a (3.2) and 3, 2 (e) Next, calculate these two numbers v1 = (3.2) yatt er v2 = Con (3.2) T(3,2)

Answer 1

Answer 7

a)

f(x,a) = 40 - 3xa

g(x) = 10 + 7x

when these functions intersects f(x,a) = g(x)

=> 40 - 3xa = 10 + 7x

=> 30 = x(3a + 7)

=> x = 30/(3a + 7)

b) When they intersect.

f(a) = g(a) = (30a + 280)/(3a + 7)

c)

Here

f(x,a) = 40 - 3xa

=>

(a) f(x, a) = 40 - 3xa g(x) = 10 + 7x when these functions intersects f(x, a) = g(x) rightdoublearrow 40 - 3xa = 10 + 7x rightdoublearrow 30 = x(3a + 7) rightdoublearrow x = 30/(3a + 7) b) When they intersect. f(a) = g(a) = (30a + 280)/(3a + 7) c) Here f(x, a) = 40 - 3xa rightdoublearrow partial differential f/partial differential x = -3 also partial differential f/partial differential a = -3 (d) As calculated above partial differential f/partial differential x = partial differential f/partial differential a = -3 for any (x, a) Hence when x = 3 and a = 2 partial differential f (3, 2)/partial differential x = partial differential f (3, 2)/partial differential a = -3

Also

d)

As calculated above

for any (x,a)

Hence when x = 3 and and a = 2