Question

The x y coordinate plane is given. The curve begins at the origin, goes up and right becoming less steep, the curve changes direction at (1, 3), goes down and right becoming more steep, passes through (2, 2),goes down and right becoming less steep, changes directions at (3, 1), goes up and right becoming more steep, passes through the point (4, 3), goes up and right becoming less steep, passes through (5, 4) almost horizontally, goes up and right becoming more steep, passes through the approximate point (6, 4.2) and ends at (7, 6). (a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)

Answer 1

The curve is increasing from the origin to (3, 1) and from (4, 3) to (7, 6). The interval(s) on which the curve is increasing is [0, 3) and [4, 7].

Step-by-step explanation:

The curve described in the question starts at the origin, goes up and to the right becoming less steep until it changes direction at (1, 3), then goes down and to the right becoming more steep until it passes through (2, 2). It then goes down and to the right becoming less steep until it changes direction again at (3, 1), then goes up and to the right becoming more steep until it passes through (4, 3). Finally, it goes up and to the right becoming less steep until it passes through (5, 4), continues almost horizontally to (6, 4.2) and ends at (7, 6).

The interval(s) on which the curve is increasing is determined by looking for intervals where the slope is positive. From the given information, we can see that the curve is increasing from the origin to (3, 1) and from (4, 3) to (7, 6). Therefore, the interval(s) on which the curve is increasing is [0, 3) and [4, 7].