Part 4/6:
If a curve is initially concave downwards and begins to rise, at the changeover point, we label this critical moment as the inflection point.
Graphically, if you observe the slope decreasing and then increasing, the inflection point is where this transition occurs.
The Second Derivative Test for Local Extrema
The second derivative test aids in identifying local maxima and minima within a function. To apply the test, follow these steps:
Determine Critical Points: Find where the first derivative ( f'(c) = 0 ).
Examine the Second Derivative:
If ( f''(c) > 0 ): The function has a local minimum at ( c ).
If ( f''(c) < 0 ): The function has a local maximum at ( c ).