sketch the graph of a function f that has a local maximum value at x = b where f(b) is undefined. choose the…
sketch the graph of a function f that has a local maximum value at x = b where f(b) is undefined. choose the correct graph below.
Answer
Explanation:
Step1: Recall local - maximum and derivative concept
A local maximum occurs when the function changes from increasing to decreasing. If $f^{\prime}(b)$ is undefined, it means there is a sharp corner, cusp, or vertical tangent at $x = b$.
Step2: Analyze each option
- Option A: At $x = b$, the function has a local minimum, not a local maximum.
- Option B: At $x = b$, the function has a local maximum and the graph has a sharp corner at $x = b$ where the derivative is undefined.
- Option C: At $x = b$, the function has a local maximum but the derivative is zero (smooth - topped peak).
- Option D: At $x = b$, the function has a local minimum, not a local maximum.
Answer:
B.