SOLUTION: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+8x+12, where x is the number of days since the concert was first announ
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Question 164164: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+8x+12, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
Answer by alicealc(293) (Show Source): You can put this solution on YOUR website!
N(x)=-0.4x^2+8x+12
we can use differentiation for this problem to find the optimum value
the optimum value is reached when
-0.4*2*x + 8 = 0
<=> -0.8x + 8 = 0
<=> -0.8x = -8
<=> x = 8/0.8 = 10
because the coefficient of x^2 is negative, the function will have a maximum value.
the maximum value is:
N(10) = -0.4*100 + 80 + 12
= -40 + 80 + 12
= 52
or in another way, to find the maximum or minimum value of a quadratic function, this formula can be used:
because the coefficient of x^2 is negative, the function will have a maximum value.
the maximum value = ->
from the function above, the value of a = -0.4, b = 8, c = 12
so the maximum value
=
=
= 83.2/1.6
= 52
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