Find the Critical Points f(x)=x^6-6x^5

Problem

ƒ(x)=x6−6*x5

Solution

1. Find the derivative of the function using the power rule.

d(ƒ(x))/d(x)=6*x5−30*x4

2. Set the derivative equal to zero to find the critical points where the slope of the tangent line is zero.

6*x5−30*x4=0

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

6*x4*(x−5)=0

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

6*x4=0⇒x=0

x−5=0⇒x=5

Final Answer

x=0,5

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