Find the Critical Points f(x)=x^4-6x^2

Problem

ƒ(x)=x4−6*x2

Solution

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

d(ƒ(x))/d(x)=4*x3−12*x

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

4*x3−12*x=0

3. Factor the expression by taking out the greatest common factor, which is 4*x

4*x*(x2−3)=0

4. Solve for x by setting each factor equal to zero.

4*x=0⇒x=0

x2−3=0⇒x2=3⇒x=±√(,3)

Final Answer

x=0,√(,3),−√(,3)

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