Final answer:
The critical points of the function are x = -3, 0, and 5, while the points of inflection are x = -2, 1, and 3.
Step-by-step explanation:
a) The critical point(s) at x = -3, 0, and 5.
Transition points refer to the values of x where a function changes behavior. In this case, critical points indicate where the derivative of the function is zero or undefined. To find the critical points, you can set the derivative of the function equal to zero and solve for x. If the derivative is undefined at a certain x-value, that is also a critical point.
So, the critical points for this function are x = -3, 0, and 5.
b) The point(s) of inflection at x = -2, 1, and 3.
Point(s) of inflection indicate where the concavity of the function changes. To find the points of inflection, you can set the second derivative of the function equal to zero and solve for x. If the second derivative changes sign at a certain x-value, that is a point of inflection.
Therefore, the points of inflection for this function are x = -2, 1, and 3.
c) The critical point(s) at x = -2, 0, and 5.
d) The point(s) of inflection at x = -3, 2, and 4.