Solve the Problem $R ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x$

question 49

Essay

Solve the problem.
-Given $R ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x$ and $C ( x ) = 2 x ^ { 2 } + 24$ where $x$ represents the number of items produced in hundreds, $R( \mathrm { x } )$ and $\mathrm { C } ( \mathrm { x } )$ represent revenue and cost in thousands of dollars. where x represents the number of items produced in hundreds, R(x)
a)Find P(x).
b)Find P(0), R(0), and C(0)and interpret each of these.
c)Find the break-even point (value wherehere $P ( x ) = 0 ) \text { if } 0 < x < 4 \text {. }$ d)For what values of x ist values of x is $\mathrm { P } ( \mathrm { x } ) > 0 \text { if } 0 < x < 4 ?$ e)For what values of x ist values of x is $P ( x ) < 0 \text { if } 0 < x < 4 ?$ f)Interpret the results from parts d)and e).

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