Give the local extreme values of f The correct choices are:
Local Extreme Values: Option C: Local maximum is q, local minima are b and d.
Give the absolute extreme values of f The correct choices are:
Absolute Extreme Values: Option C: There is no absolute extreme value.
Local Extreme Values:
Analyze the Given Information: Review the descriptions of local maximum and minimum values for function
Local maximum: q
Local minima: b and d
Compare Descriptions with Options:
Option A states there are no local extrema, which contradicts the provided information.
Option B incorrectly identifies local maxima as b and d, and the local minimum as q, conflicting with the given details.
Option C correctly aligns with the information provided, indicating a local maximum at q and local minima at b and d.
Absolute Extreme Values:
Consider the Absence of Constraints: No specific constraints or range are given for function
.
Evaluate the Options:
Option A claims the absolute maximum value is b, which isn't supported by the information provided.
Option B suggests the absolute minimum is q, which doesn't match the given details.
Option C concludes there is no absolute extreme value. Without constraints or a specific range, the function may not reach an absolute maximum or minimum, aligning with the absence of explicitly defined extreme values.
These conclusions are derived by matching the provided information with the options presented, resulting in Option C being consistent with the given details for both local extreme values and absolute extreme values of function
.