Differentiation and Properties of curves

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Mathematics

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Explanation & Answer

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).


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