Finall answer:
The function is increasing in intervals b. (a, b) and (b, ∞).
Step-by-step explanation:
In calculus, determining where a function increases involves examining its derivative. When the derivative is positive, the function is increasing. For this particular function, the intervals where it's increasing can be identified by analyzing its derivative and finding where it's greater than zero. In this case, it's increasing where the derivative is positive, which means where the function is moving upwards.
The interval (a, b) indicates that for all x-values between 'a' and 'b', the function is on the rise. Similarly, in the interval (b, ∞), the function continues to increase for all x-values greater than 'b'. These intervals represent the regions on the x-axis where the function is consistently climbing, showcasing an upward trend.
Therefore the correct answer is b.