Final Answer:
The function is increasing at points A and E. (Option B)
Step-by-step explanation:
To determine where the function is increasing, we examine the slope of the function at different points. If the slope is positive, the function is increasing. In the given options, points A and E correspond to regions where the function has a positive slope.
The slope of a function at a point is given by its derivative. If f'(x) > 0, the function is increasing at that point. In calculus, this is referred to as the first derivative test. By calculating the derivatives of the function at points A and E, we can verify that the derivatives are positive, indicating an increasing function.
In mathematical terms, if f'(A) > 0 and f'(E) > 0, where f'(x) is the derivative of the function with respect to x, then the function is increasing at points A and E. This is a fundamental concept in calculus to analyze the behavior of functions at specific points.(Option B)"