P(X) = -60X2 + 1500X - 4000 - 1 ≤ x ≤ 25
This is the profit function and its domain,
can you please help me find
1) the value of X where there is a breakeven point
2) the value of X where profit be maximum
thankyou so very much!!!
The breakeven point is the point where there is no profit and no deficit. In other words, the poitns when $\displaystyle P(x) = 0 $. You find x values of this by finding the roots of the equation. Using the quadratic formula!
$\displaystyle P(x) = -60x^2+1500x-4000 = 0 $
$\displaystyle x = \frac{-1500 \pm \sqrt{1500^2-4(-60)(-4000)}}{2(-60)} $
$\displaystyle x = \frac{-1500 \pm \sqrt{1290000}}{-120} $
$\displaystyle x = 3.035 $ or $\displaystyle x = 21.964 $
For the maximum, the first derivative of the function is 0. Solve for x, and then plug that x value into the original equation to find P(x) for that value of x. The 2nd derivative test will tell you whether you have a maximum or a minimum. (Although you will have a maximum, since your coefficients of x^2 is negative!)