The function f(x)=-x^4+6x^2+8xhasx=-1 as a critical number. The point (-1,-1) on the graph of y=f(x) is (i) local maximum (ii) local minimum (iii) point of inflexion (i) is true (ii) is true. (iii) is true. (i), (ii), (iii) are all true. none of these is true.

## Step 1: Find the first derivative### We need to find the first derivative of the function . Using the power rule, we get .## Step 2: Find the second derivative### Now, we find the second derivative of the function, which is .## Step 3: Evaluate the second derivative at the critical point### We are given that is a critical number. We evaluate the second derivative at this point: .## Step 4: Analyze the second derivative### Since the second derivative at is 0, the second derivative test is inconclusive. We need to analyze the behavior of the function around the critical point.## Step 5: Further analysis using the first derivative### Let's analyze the sign of the first derivative around . For , . For , . For , . Since the first derivative doesn't change sign around , and , we have a possible inflection point.## Step 6: Check for inflection point### Since , we check the concavity around . We found . For (e.g., ), (concave up). Since the concavity changes around , it is an inflection point.