Q. 24 - 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 at point $\left(0·5, -0·5\right)$ and local minimum at point $\left(1·5,-3·5 \right)$ .

Step 1. Given information .

Consider the given graph .

Step 2. Classifying local 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 $\left(0·5,-0·5\right)$ that is the local maximum point of the graph and point $\left(1·5, -3·5\right)$ is the local minimum point of the graph .