Find the Critical Points x^3-3x+1

Problem

ƒ(x)=x3−3*x+1

Solution

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

(d(x3)−3*x+1)/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 zero.

3*x2−3=0

3. Factor out the greatest common factor from the equation.

3*(x2−1)=0

4. Solve for x by factoring the difference of squares or isolating the variable.

x2−1=0

x2=1

x=±1

Final Answer

x=−1,1

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