Find the Critical Points f(x)=x^4-2x^3

Problem

ƒ(x)=x4−2*x3

Solution

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

d(ƒ(x))/d(x)=4*x3−6*x2

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

4*x3−6*x2=0

3. Factor the expression by taking out the greatest common factor, which is 2*x2

2*x2*(2*x−3)=0

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

2*x2=0⇒x=0

2*x−3=0⇒x=3/2

5. Identify the critical points as the xvalues found in the previous step, as the derivative is defined for all real numbers.

x=0,3/2

Final Answer

Critical Points: *x=0,3/2

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