Expert: Ahmed Salami - 4/27/2009

Question
how to I get the maximun profit of -.01x^3+.3x^2+15x-100

Answer
Hi Andrea,
The maximum value of -0.01x^3 + 0.3x^2 + 15x - 100 occurs when its first derivative equals zero and its second derivative is negative.
The first derivative is -0.03x^2 + 0.6x + 15, equating to zero
-0.03x^2 + 0.6x + 15 = 0
dividing through by -0.03
x^2 - 20x - 500 = 0
The roots of this quadratic equation are approximately -14.5 and 34.5
The second derivative is -0.06x + 0.6, checking its values at the two points;
at x = -14.5, we have -0.06(-14.5) + 0.6 = 1.47
at x = 34.5, we have -0.06(34.5) + 0.6 = -1.47
And so we can see that the maximum occurs at x = 34.5

Regards