Q. 23

Question


For the graph of f in the given figure , approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points .

Step-by-Step Solution

Verified
Answer

The f has a local maximum at point x=1·5 .

1Step 1. Given information .


Consider the given graph .

2Step 2. Classifying maximum and minimum value .

To classify the maximum and minimum value in the graph of a function if the graph is  smooth and unbroken, then somewhere between each root of f the function must turn around, and at that turning point it must have a local extremum with a horizontal tangent line .

In the given graph the turning point is at x=0·5 that is the local maximum point of the graph with roots 0,4 where x0,4 .