Find the Critical Points f(x)=2x^3-12x^2-72x+2017

Problem

ƒ(x)=2*x3−12*x2−72*x+2017

Solution

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

d(ƒ(x))/d(x)=6*x2−24*x−72

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

6*x2−24*x−72=0

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

x2−4*x−12=0

4. Factor the quadratic equation to solve for the values of x

(x−6)*(x+2)=0

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

x−6=0⇒x=6

x+2=0⇒x=−2

Final Answer

x=6,−2

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