Find the Critical Points x+1/x

Problem

ƒ(x)=x+1/x

Solution

1. Define the function and identify its domain. The function is ƒ(x)=x+1/x which is defined for all x≠0

2. Find the derivative of the function with respect to x Using the power rule where 1/x=x(−1) the derivative is:

d(ƒ(x))/d(x)=1−1/(x2)

3. Set the derivative to zero to find potential critical points.

1−1/(x2)=0

4. Solve for x by isolating the variable.

1=1/(x2)

x2=1

x=±1

5. Check for undefined points in the derivative. The derivative d(ƒ(x))/d(x)=1−1/(x2) is undefined at x=0 However, x=0 is not in the domain of the original function, so it is not a critical point.

Final Answer

x=1,−1

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