Expert: Alon Mandes - 11/12/2009

Question
QUESTION: 1)A firm's demand curve for a product is given as P=300-25Q
a. What in you view is the total revenue function of that product?
b. Is it possible to finc the marginal revenue function of that product? If so, what is it?
c. At What price should the firm sell this product in order to generate the  highest level of revenue (from that product)?


2) Given that f(x) = (1/3)x^3 + (5/2)x^2 - 14x + 5
a. At What point(s) in the domain is f(x) stationary?
b. Over what interval in the domain is f(x) increasing?
c. What type of function would the third derivative of f(x) be classified as?

ANSWER: 1) Is out of my expertise .

2) f(x) = (1/3)x^3 + (5/2)x^2 - 14x + 5 . Let's derive & solve f'=0 :
f'(x)=x^2+5x-14
f'(x)=0 --> x^2+5x-14=0 , solutions : x1=2 & x2=-7 . Let's find which is min & which is max :
f''(x)=2x+5
f''(2)=9 >0 that means x=2 is min
f''(-7)=-19 <0 that means x=-9 is max
Therefore :
f(x) is increasing in the interval x<-9 or x>2 .
f'''(x)=2 . This is a constant function .

Alon.


---------- FOLLOW-UP ----------

QUESTION: Ok, thanks much. but how did u arrive at the solution
f'(x) = x^2 + 5x - 14?

ANSWER: The derivative of a polynom f(x)=a1x+a2x^2+a3x^3+...+anx^n is
f'(x)=a1+2a2x+3a3x^2+...+an*n*x^(n-1) .

Alon.

---------- FOLLOW-UP ----------

QUESTION: SOrry to bother you but i really do not get it. could u explain a little further? thanks.  

Answer
If we have a function that is polynom such as : f(x)=ax²+bx+c then the derivative will be :
f'(x)=2ax+b.
If we have a function that is polynom such as : f(x)=ax³+bx²+cx+d then the derivative will be :
f'(x)=3ax²+2bx+c.
The rule is : (Ax^n)'=nAx^(n-1) .

Alon.