Questions: (a) Determine the domain.
(-∞, ∞) (Type your answer in interval notation)
(b) Determine all local minimum points, and tell if any is an absolute minimum point.
Select the correct choice below and, If necessary, fill in the answer box(es) to complete your choice.
A. The local minimum point(s) is/are and the absolute minimum point(s) is/are 1.
(Type an ordered pair, using integers or decimals, Round to the nearest hundredth as needed. Use a comma to separate answers as needed).
B. The local minimum point(s) is/are and there is no absolute minimum point.
(Type an ordered pair, using integers or decimals. Round to the nearest hundredth as needed. Use a comma to separate answers as needed)
Transcript text: (a) Determine the domain.
$(-\infty, \infty)$ (Type your answer in interval notation)
(b) Determine all local minimum points, and tell if any is an absolute minimum point.
Select the correct choice below and, If necessary, fill in the answer box(es) to complete your choice.
A. The local minimum point(s) is/are $\square$ and the absolute minimum point(s) is/are $\square$ 1.
(Type an ordered pair, using integers or decimals, Round to the nearest hundredth as needed. Use a comma to separate answers as needed).
B. The local minimum point(s) is/are $\square$ and there is no absolute minimum point.
(Type an ordered pair, using integers or decimals. Round to the nearest hundredth as needed. Use a comma to separate answers as needed)
Solution
Solution Steps
Step 1: Determine the domain
The domain of a function is the set of all possible input values (x-values). The graph extends infinitely to the left and right.
Step 2: Determine Local Minimum Points
Local minimum points are points where the function changes from decreasing to increasing. Graph D has two such points.
Step 3: Determine Absolute Minimum Point
An absolute minimum point is the lowest point on the entire graph. Since the graph extends downwards infinitely, there isn't a single lowest point.
Final Answer:
Domain: (-∞, ∞)
Local Minimums: There are two local minimums. Option B is correct, but more information is needed to determine their x,y coordinates.