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 .

Short answer

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

Step-by-step solution

Step 1. Given information .

Consider the given graph .

Step 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$\left(0,4\right)$where$x\in \left(0,4\right)$.