F(x)= mx³-3mx²+(2m+1)x+3-m, find m so that f(x) has max and min , and that they are colinear with the origin.?

I found y'=3mx² -6mx+2m+1 for f(x) to have both max and min, f'(x) should have two solutions, so ▲>0 ▲>0, m(12m+12)>0 so either both m and (12m+12) are positive or negative. positive m>0, and 12m+12>0,==> m>1 negative m<0, 12m+12<0, ==>m< -1 so from that I... hiển thị thêm I found
y'=3mx² -6mx+2m+1
for f(x) to have both max and min, f'(x) should have two solutions, so ▲>0
▲>0,
m(12m+12)>0
so either both m and (12m+12) are positive or negative.
positive
m>0, and 12m+12>0,==> m>1
negative
m<0, 12m+12<0, ==>m< -1
so from that I conclude either m>0 or m<-1
how do I line them up with the origin, make them Max/Min colinear with the origin.
thanks for your input.
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