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Q. 24

Expert-verified
Found in: Page 248

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# 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.

The f has local maximum at point $\left(0·5,-0·5\right)$ and local minimum at point $\left(1·5,-3·5\right)$ .

See the step by step solution

## 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 .