Find the Critical Points f(x)=x^4-4x^3+10

Problem

ƒ(x)=x4−4*x3+10

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*x2

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*x2=0

3. Factor the expression by taking out the greatest common factor, which is 4*x2

4*x2*(x−3)=0

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

4*x2=0⇒x=0

x−3=0⇒x=3

Final Answer

x=0,3

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