Differentiation and Properties of curves

label Calculus
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Apr 9th, 2015

P(x) = x(1284 - 0.19 x^2) - 810 - 380 x = -810 + 904 x - 0.19 x^3. In what follows the function P(x) will be considered for all real numbers.

P '(x) = 904 - 0.57x^2. The points where P '(x) = 0 are x = +- sqrt(904/0.57) = +- 39.8  

(A) The average of x values is 39.8

(B) The average of x values is - 39.8.

(C) P ''(x) = -1.14x > 0 when x < 0   concave up on (-l 0)

(D) concave down on (0, l).

Apr 8th, 2015

b, c, and d did not come out correct

Apr 8th, 2015

The profit function does not make sense for negative values of x. I assumed that it would be considered for all real x. In this case, there is no local minimum (no point where P'(x) = 0) and in (B) put -1000.

(C) P(x) is concave up nowhere.

(D) P(x) is concave down on (0, l).

Apr 8th, 2015

concave down (D) is still incorrect...the others are all good

Apr 9th, 2015

It should be concave down on 0 < x < infty or (0, I). Which letter did you input for infinity, I ("eye")capital or 

l (el) small?

Apr 9th, 2015

sorry I mistook that for the number 1...Thank you so much

Apr 9th, 2015

You are welcome.

Apr 9th, 2015

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Apr 9th, 2015
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