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 where 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
In option A, the function has a local minimum at $x=a$ and a local maximum at $x = b$ where the graph has a sharp corner (so $f^{\prime}(b)$ is undefined). In option B, the function has a local minimum at $x = b$. In option C, the function has a local minimum at $x=a$ and the function is smooth at $x = b$ (so $f^{\prime}(b)$ is defined). In option D, the function has a local minimum at $x=a$ and the function is smooth at $x = b$ (so $f^{\prime}(b)$ is defined).
Answer:
A.