Find the Critical Points f(x)=x^3-3x+1

Problem

ƒ(x)=x3−3*x+1

Solution

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

d(ƒ(x))/d(x)=3*x2−3

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

3*x2−3=0

3. Solve for x by first factoring out the greatest common factor.

3*(x2−1)=0

4. Factor the difference of squares to isolate the roots.

3*(x−1)*(x+1)=0

5. Identify the critical values by setting each factor containing x to zero.

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x=1,−1

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