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

Problem

ƒ(x)=3*x2+2*x3

Solution

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

d(ƒ(x))/d(x)=6*x+6*x2

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

6*x+6*x2=0

3. Factor the expression to solve for the variable x

6*x*(1+x)=0

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

6*x=0⇒x=0

1+x=0⇒x=−1

Final Answer

x=0,−1

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