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

Problem

ƒ(x)=3*x(2/3)−2*x

Solution

1. Find the derivative of the function using the power rule.

d(ƒ(x))/d(x)=3⋅2/3*x(−1/3)−2

2. Simplify the derivative expression.

ƒ(x)′=2*x(−1/3)−2

3. Rewrite the derivative using a positive exponent to identify where it is undefined.

ƒ(x)′=2/√(3,x)−2

4. Identify where the derivative is undefined.

x=0

5. Set the derivative to zero to find stationary points.

2/√(3,x)−2=0

6. Solve for x by isolating the radical term.

2/√(3,x)=2

√(3,x)=1

x=1

Final Answer

Critical Points: *x=0,x=1

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