for each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an…
for each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum. (enter your answers as a comma - separated list.)\nabsolute maximum\nnone\n×\nabsolute minimum\nnone\n×\nlocal maximum\na,c\n×\nlocal minimum\nb,d,r\n×\nneither a maximum nor a minimum\ns\n×
Answer
Explanation:
Step1: Define absolute maximum
The highest - point of the entire function. Since the graph has no highest - point shown (it could potentially go higher outside the shown domain), there is no absolute maximum.
Step2: Define absolute minimum
The lowest - point of the entire function. Since the graph has no lowest - point shown (it could potentially go lower outside the shown domain), there is no absolute minimum.
Step3: Identify local maximum
A local maximum is a point where the function changes from increasing to decreasing. At (x = a) and (x = c), the function changes from increasing to decreasing, so (a,c) are local maxima.
Step4: Identify local minimum
A local minimum is a point where the function changes from decreasing to increasing. At (x = b), (x = d), and (x = r), the function changes from decreasing to increasing, so (b,d,r) are local minima.
Step5: Identify neither maximum nor minimum
At (x = s), the function is neither at a peak (local maximum) nor at a valley (local minimum), so (s) is neither a maximum nor a minimum.
Answer:
absolute maximum: none absolute minimum: none local maximum: (a,c) local minimum: (b,d,r) neither a maximum nor a minimum: (s)