For what value(s) of X does f(x)=(e^x)/(x) has a local maximum? There is no local maximum 0 (1)/(2) 2 1

## Step 1: Find the derivative of the function### To find the local maximum or minimum, we need to find the critical points by taking the derivative of the function and setting it to zero. The derivative of is given by the quotient rule: .## Step 2: Find the critical points### Set the derivative equal to zero and solve for x: . This implies . Since is never zero, we have , so .## Step 3: Determine if the critical point is a maximum or minimum### To determine if the critical point is a local maximum or minimum, we can use the second derivative test. The second derivative is . Evaluating the second derivative at , we get . Since the second derivative is positive at , the function has a local minimum at .