It is known that x = 1 is an extreme point of the function f (x) = mx3-3 (M + 1) x2 + NX + 1, where m, n ∈ R It is known that x = 1 is an extreme point of the function f (x) = mx3-3 (M + 1) x2 + NX + 1, where m, n ∈ R, M > 0 (1) Find the expression of the relationship between M and n; (2) Finding monotone interval of F (x); detailed process

It is known that x = 1 is an extreme point of the function f (x) = mx3-3 (M + 1) x2 + NX + 1, where m, n ∈ R It is known that x = 1 is an extreme point of the function f (x) = mx3-3 (M + 1) x2 + NX + 1, where m, n ∈ R, M > 0 (1) Find the expression of the relationship between M and n; (2) Finding monotone interval of F (x); detailed process

f(x)=mx3-3(m+1)x2+nx+1
f'(x)=3mx^2-6(m+1)x+n
3m-6(m+1)+n=0
n=3m-6
(2) Find the monotone interval of F (x);
f'(x)=3mx^2-6(m+1)x+n=3mx^2-6(m+1)x+3m-6
x1+x2=2(m+1)/m=2+2/m
If X1 = 1, then x2 = (M + 2) / M
x2>x1
(- ∞; 1), ((M + 2) / M; + ∞) increase (1; (M + 2) / M) decrease