These are both small questions, need accurate answers. -------------------------

Question

These are both small questions, need accurate answers.

------------------------------------------------------------------------------------------------------------------

1. Let f(2, 3) = 7    fx(2,3) = 4.             

Then the tangent plane to the surface z = f(x,y) at the point (2,3) is?

------------------------------------------------------------------------------------------------------------------

2. A small business has $300,000 worth of equipment and 100 workers. The total monthly production, P (in thousands of dollars), is a function of the total value of the equipment, V (in thousands of dollars), and the total number of workers, N. The differential of P is given by dP = 4.9dN + .5dV. If the business decides to lay off 3 workers and buy additional equipment worth $20,000, then:

a) Monthly production increases.

b) Monthly production decreases.

c) Monthly production stays the same.

**Please show work on this one.

-------------------------------------------------------------------------------------------------------------------

Explanation / Answer

1.thus equation f(x,y) satisfying fx(2,3)=4(i.e.2x) and f(2,3)=7

we get f(x,y)=x^2+y

thus fy=1

thus tangent plane at x0,y0,z0 is given by

z-z0=fx(x-x0)+fy(y-y0)

z-7=4(x-2)+(y-3)

=>4x+y-z=4

2.dP=4.9dN+0.5dV

=4.9(-3)+0.5(20)=10-14.7=-4.7

thus monthly production decreases.

ans-(b)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.