Find the Critical Points 1/x

Problem

ƒ(x)=1/x

Solution

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

2. Find the derivative of the function using the power rule. Rewrite the function as ƒ(x)=x(−1)

3. Apply the power rule to differentiate.

d(ƒ(x))/d(x)=−1⋅x(−2)

d(ƒ(x))/d(x)=−1/(x2)

4. Set the derivative equal to zero to find stationary points.

−1/(x2)=0

5. Solve for x and observe that there are no real values of x that satisfy this equation, as a fraction is only zero if its numerator is zero.

6. Identify points where the derivative is undefined. The derivative d(ƒ(x))/d(x)=−1/(x2) is undefined at x=0

7. Check the domain of the original function. Since x=0 is not in the domain of ƒ(x)=1/x it cannot be a critical point.

Final Answer

Critical Points of 1/x=None

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