Find the Critical Points x^3-3x

Problem

x3−3*x

Solution

1. Define the function and identify the goal. To find the critical points of ƒ(x)=x3−3*x we must find where the first derivative is equal to zero or undefined.

2. Differentiate the function with respect to x using the power rule.

(d(x3)−3*x)/d(x)=3*x2−3

3. Set the derivative to zero to find the stationary points.

3*x2−3=0

4. Factor the quadratic equation to solve for x

3*(x2−1)=0

3*(x−1)*(x+1)=0

5. Solve for the values of x

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x=1,−1

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