8. Given that h(7)45 one can conclude that: a) h(x) has a relative maximum at x-

Question

8. Given that h(7)45 one can conclude that: a) h(x) has a relative maximum at x-7, b) h(x) has an inflection point at x7 c) h(x) has a relative minimum at x-7 . d) hCx) has an x-intercept at x7 e) None of the above conclusions are true. 9. A company knows that x units of a product will sell at a price ofp dollars per unit. The function m x) outputs the per unit price in dollars for an input of the number of units soMa The solution to which of the following equations could find the number of unit, that will matimiz rexeaue for this company? a) x p'(x)+p(x)- b) p'(x)=0 x-p'(x)-P(x) = O c) d) p"(x) = 0 e) p(x)=0

Explanation / Answer

8. since, h'(7) = 0, so 7 is a critical point and h"(7) = 45 > 0 , hence 7 is the minima

hence, h(x) has a relative minima at x = 7 ..............(c)

9. revenue = R(x) = quantity multiplied by per unit price = x.p(x)

to maximize revenue we have, R'(x) = x.p'(x) + p(x) = 0 .................. (a)

and, R"(x) = x.p"(x) + 2.p'(x) > 0

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