Find the Critical Points f(x)=x^3-6x^2+15

Problem

ƒ(x)=x3−6*x2+15

Solution

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

d(ƒ(x))/d(x)=3*x2−12*x

2. Set the derivative equal to zero to find the values of x where the slope of the tangent line is zero.

3*x2−12*x=0

3. Factor the expression to solve for the variable x

3*x*(x−4)=0

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

3*x=0⇒x=0

x−4=0⇒x=4

Final Answer

x=0,4

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