Find the Critical Points f(x)=2x^3-9x^2+12x

Problem

ƒ(x)=2*x3−9*x2+12*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*x2−18*x+12

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

6*x2−18*x+12=0

3. Factor out the greatest common factor to simplify the quadratic equation.

6*(x2−3*x+2)=0

4. Factor the quadratic expression inside the parentheses by finding two numbers that multiply to 2 and add to −3

6*(x−1)*(x−2)=0

5. Solve for x by setting each linear factor equal to zero.

x−1=0⇒x=1

x−2=0⇒x=2

Final Answer

x=1,2

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