Find the Critical Points f(x)=2x^3-3x^2-36x+5

Problem

ƒ(x)=2*x3−3*x2−36*x+5

Solution

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

d(ƒ(x))/d(x)=6*x2−6*x−36

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

6*x2−6*x−36=0

3. Simplify the equation by dividing all terms by the greatest common factor, which is 6

x2−x−6=0

4. Factor the quadratic equation to solve for the variable x

(x−3)*(x+2)=0

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

x−3=0⇒x=3

x+2=0⇒x=−2

Final Answer

x=3,−2

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