maxima and minima\nquestion 3, 4.1.7\npoints: 0 of 1\nsketch the graph of a function f that has a local…
maxima and minima\nquestion 3, 4.1.7\npoints: 0 of 1\nsketch the graph of a function f that has a local minimum value where f(b)=0.\nchoose the correct graph below.
Answer
Explanation:
Step1: Recall derivative - minimum relation
At a local minimum of a differentiable function, the derivative is zero and the function changes from decreasing to increasing.
Step2: Analyze each graph
In option A, at (x = b), the function has a local maximum since it changes from increasing to decreasing. In option B, at (x = b), the function has a local maximum. In option C, at (x = b), the function has a local minimum as it changes from decreasing to increasing and (f^{\prime}(b)=0). In option D, at (x = b), the function has a local maximum.
Answer:
C.