the inflexion is where the slope is constant. if the slope is positive (inccreasing as you pass a pole, what is the polarity (sign) of the pole?
To determine the polarity or sign of the pole, we need to understand how the slope changes as we pass the pole.
In mathematics, the slope of a curve at a particular point is given by the derivative or the rate of change of the function with respect to that variable. If the slope is positive, it means that the value of the function is increasing as we move along the curve.
Now, when it comes to poles and their corresponding signs, it's important to consider whether the function is approaching the pole from the left or from the right.
If the slope is positive and increasing as you pass a pole from left to right, it means that the function is approaching the pole from the negative side (left) and moving towards positive values (right) after passing the pole. In this case, the pole is classified as a positive pole.
On the other hand, if the slope is positive and increasing as you pass a pole from right to left, it means that the function is approaching the pole from the positive side (right) and moving towards negative values (left) after passing the pole. In this case, the pole is classified as a negative pole.
So, to summarize:
- If the slope is positive and increasing as you pass a pole from left to right, the pole is positive.
- If the slope is positive and increasing as you pass a pole from right to left, the pole is negative.