how do i know the staionary point that im finding is minmum or maximum without using calcuaotors
There are a few ways to determine if a stationary point is a minimum or maximum without using a calculator:
1. The First Derivative Test: Calculate the first derivative of the function at the stationary point. If the derivative changes sign from positive to negative at the stationary point, it is a maximum. If the derivative changes sign from negative to positive at the stationary point, it is a minimum.
2. The Second Derivative Test: Calculate the second derivative of the function at the stationary point. If the second derivative is positive at the stationary point, it is a minimum. If the second derivative is negative at the stationary point, it is a maximum.
3. Use the graph: Plot the function and visually inspect the shape of the curve around the stationary point. If the curve is concave up, the stationary point is a minimum. If the curve is concave down, the stationary point is a maximum.