The method of discerning concavity revolves around calculating the second derivative of a given function. When the resulting value is positive, it indicates the function exhibits concave up behavior. Conversely, a negative outcome signifies a function is concave down. This process is essential in pinpointing the maximum or minimum values of the function, which are key to comprehending its complete behavior.
| Topic | Problem | Solution |
|---|---|---|
| None | Let's consider the function \(f(x) = 2x^3 - 9x^2 … | First, we find the first derivative of the function: \(f'(x) = 6x^2 - 18x + 12\) |