Find the Critical Points f(x)=2x^3-24x

Problem

ƒ(x)=2*x3−24*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*x2−24

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

6*x2−24=0

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

6*(x2−4)=0

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

x2−4=0

x2=4

x=±2

Final Answer

x=−2,2

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