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

Problem

ƒ(x)=2*x3−6*x

Solution

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

d(ƒ(x))/d(x)=6*x2−6

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

6*x2−6=0

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

6*(x2−1)=0

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

x2−1=0

x2=1

x=±1

5. Identify the critical points as the xvalues where the derivative is zero or undefined (since the derivative is a polynomial, it is defined everywhere).

x=1,x=−1

Final Answer

Critical Points: *x=1,−1

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