Question 1119978
.
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    {{{graph( 330, 330, -1.5, 10.5, -5.5, 20.5,
          -4x^3+10x^2+8x-6, 18
)}}}


  Plot y = {{{-4t^3+10t^2+8t-6}}} (red)  and y = 18 (green)



1.  Take the derivative  y'(t) = -12t^2 + 20t + 8.


2.  Equate it to zero:  -12t^2 + 20t + 8 = 0,  or, equivalently,

    3t^2 - 5t - 2 = 0


3.  Solve the quadratic equation  {{{t[1,2]}}} = {{{(5 +- sqrt(5^2 + 4*3*2))/(2*3)}}} = {{{(5 +- sqrt(49))/6}}}.


    Take its positive root  {{{t[1]}}} = {{{(5 + 7)/6}}} = 2.


4.  Substitute t = 2 into your polynomial P(t) to check the value of the profit

    P(2) = {{{-4*2^3+10*2^2+8*2-6}}} = 18.


<U>Answer</U>.   In two years.
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