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

Problem

ƒ(x)=3*x3−36*x

Solution

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

d(ƒ(x))/d(x)=9*x2−36

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

9*x2−36=0

3. Factor out the greatest common factor from the equation.

9*(x2−4)=0

4. Solve for x by factoring the difference of squares or by isolating the variable.

x2−4=0

x2=4

x=±2

5. Identify the critical points as the xvalues where the derivative is zero (the derivative is defined for all real numbers, so there are no points where it does not exist).

x=2,x=−2

Final Answer

Critical Points: *x=2,−2

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