請問點計daily function (profit=revenue-cost),請盡量加以長解,thx

A one-product firm estimates that its daily function is C(x)=x3-6x2+13x+15 and its total revenue function is R(x)=28x. Find the value of x that maximizes the daily profit (profit=revenue-cost ).
利潤：
P(x)=28x - x3-6x2+13x+15
= -x3 +6x2 +15x – 15
求極值
dx/dt = -3x2 + 12x + 15 = 0
-3(x2 – 4x – 5) = 0
-3(x – 5)(x + 1) = 0
所以 x = 5 及 x = -1 是有極值
但 x 不可能為負值，所以當
x = 5時它的數值為極大。
極大值為
P(x)= -x3 +6x2 +15x – 15
= -(5)3 +6(5)2 +15(5) – 15
= 85