Q. 26 - Calculus

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

Answer

The f has local maximum point at $\left(2 , 1·5\right)$ and $\left(2, 0·5\right)$ .

Step 1. Given information .

Consider the given graph .

Step 2. Classifying the maximum and local points .

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 points are  at $\left(2 ,1·5\right)$ and $\left(2, 0·5\right)$ these are the maximum local points .