identify the local maximum and local minimum of the function shown in the graph below.
identify the local maximum and local minimum of the function shown in the graph below.
Answer
Explanation:
Step1: Recall local - extrema definition
Local maximum is a point where the function value is greater than the values at nearby points, and local minimum is a point where the function value is less than the values at nearby points.
Step2: Observe the graph
By looking at the graph, we find the peak and valley points. The function has a peak near (x=- 1) and a valley near (x = 2).
Step3: Determine the coordinates
At (x=-1), the (y) - value of the function is (y = 1). At (x = 2), the (y) - value of the function is (y=-3).
Answer:
Local maximum: ((-1,1)); Local minimum: ((2,-3))