Find the Critical Points f(x)=x^3-3x^2

Problem

ƒ(x)=x3−3*x2

Solution

1. Find the derivative of the function ƒ(x) using the power rule.

d(ƒ(x))/d(x)=3*x2−6*x

2. Set the derivative equal to zero to find the critical points where the slope of the tangent line is zero.

3*x2−6*x=0

3. Factor the expression by taking out the greatest common factor, which is 3*x

3*x*(x−2)=0

4. Solve for x by setting each factor equal to zero.

3*x=0⇒x=0

x−2=0⇒x=2

Final Answer

x=0,2

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