Final answer:
To find the intervals on which a function is increasing, we examine the derivative. Critical points are found by solving f'(x) = 0. Intervals of concavity are determined by the second derivative, and inflection points occur where the concavity changes.
So, the correct answer is: b) Critical points
Step-by-step explanation:
To find the intervals on which a function is increasing, we need to examine the derivative of the function. If the derivative is positive, then the function is increasing. If the derivative is negative, then the function is decreasing.
To find the critical points, we need to solve the equation f'(x) = 0. These are the points where the function changes from increasing to decreasing or vice versa.
To determine the intervals of concavity, we need to examine the second derivative of the function. If the second derivative is positive, then the function is concave up. If the second derivative is negative, then the function is concave down.
Inflection points occur where the concavity changes from up to down or vice versa. They can be found by solving the equation f''(x) = 0.