Find the Critical Points x+4/x

Problem

ƒ(x)=x+4/x

Solution

1. Define the function and its domain. The function is ƒ(x)=x+4/x which is defined for all x≠0

2. Find the derivative of the function with respect to x Using the power rule, where 4/x=4*x(−1)

d(ƒ(x))/d(x)=1−4/(x2)

3. Set the derivative to zero to find the stationary points where the slope is horizontal:

1−4/(x2)=0

4. Solve for x by isolating the variable:

1=4/(x2)

x2=4

x=±2

5. Identify critical points by checking where the derivative is zero or undefined. The derivative is undefined at x=0 but since x=0 is not in the domain of the original function, it is not a critical point. The critical points are x=2 and x=−2

Final Answer

x=−2,2

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