- #1
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Homework Statement
Determine how many real numbers satisfy the equation x3-6x2+1=0. Give reasons for your answer naming any theorems you use.
2. The attempt at a solution
let:f(x)=x3-6x2+1
→f'(x)=3x2-12x
for stationary points:f'(x)=0
→3x(x-4)=0
∴x=0 or x=4
to determine if minimum or maximum points:
f''(x)=6x-12
→f''(0)=-12<0
→f''(4)=12>0
∴(0,1) is a maximum point.
∴(4,-31) is a minimum point.
Not sure how to finish. I know it has 3 solutions, but I'm not sure as how to express my answer in the correct format. Help?
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