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Found in: Page 208

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# Use the graph to state the absolute and local maximum and minimum values of the function.

Absolute maximum occurs at $$f(4) = 5$$. There is no absolute minimum value. Local maximum occurs at $$f(4) = 5$$, $$f(6) = 4$$. Local minimum occurs at $$f(2) = 2,f(1) = 3$$, $$f(5) = 3$$.

See the step by step solution

## Step 1: Given data

The given function is the graph.

## Step 2: Concept of Differentiation

Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.

## Step 3: Simplify the expression

Absolute maximum occurs at $$f(4) = 5$$ because $$f(4) \ge f(x)$$ for all value of $$x$$ in a domain.

The open dot in the graph indicates that the point is not included in the domain. So, the point $$x = 7$$ is not included in the domain. Thus, the minimum value does not occur at the point and hence there is no absolute minimum value.

Since $$f(4) \ge f(x)$$ for any $$x$$ nearer to 4 in a domain and $$f(6) \ge f(x)$$ for any $$x$$ nearer to 6 in a domain, local maximum occurs at $$f(4) = 5$$ and $$f(6) = 4$$.

Since $$f(2) \le f(x)$$ for any $$x$$ nearer to 2 in a domain, $$f(1) \le f(x)$$ for any $$x$$ nearer to 1 in a domain, and $$f(5) \le f(x)$$ for any $$x$$ nearer to 5 in a domain, local minimum occurs at three points such as $$f(2) = 2,f(1) = 3$$ and $$f(5) = 3$$.