Find the Critical Points x^3+3x^2-144x

Problem

ƒ(x)=x3+3*x2−144*x

Solution

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

d(ƒ(x))/d(x)=3*x2+6*x−144

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

3*x2+6*x−144=0

3. Divide by the greatest common factor to simplify the quadratic equation.

x2+2*x−48=0

4. Factor the quadratic expression by finding two numbers that multiply to −48 and add to 2

(x+8)*(x−6)=0

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

x+8=0⇒x=−8

x−6=0⇒x=6

Final Answer

x=−8,6

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