Find the Critical Points f(x)=4+1/3x-1/2x^2

Problem

ƒ(x)=4+1/3*x−1/2*x^2

Solution

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

d(ƒ(x))/d(x)=1/3−x

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

1/3−x=0

3. Solve for x by isolating the variable on one side of the equation.

−x=−1/3

x=1/3

4. Identify the critical points by noting that the derivative is defined for all real numbers, so the only critical point occurs where the derivative is zero.

x=1/3

Final Answer

x=1/3

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