定义Mf(x)=f(x+1)-f(x)为函数f(x)的边际函数,某利润P(x)=-x3+30x2+1010(x∈[10,25]且x∈N),则他的边际函数是?
热心网友
P(x+1) = -(x+1)^3+30(x+1)^2 + 1010 (x+1∈[10,25]且x+1∈N)P(x+1)-P(x)= [ -(x+1)^3+30(x+1)^2 + 1010 ] - [-x^3+30x^2 + 1010]=x^3-(x+1)^3 + 30(x+1)^2 - 30x^2= -3x^2 -3x -1 + 60x +30= -3x^2 +57x +29此即为边际函数。x的定义域为 x∈[10,24]且x∈N