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Q8E

Expert-verifiedFound in: Page 208

Book edition
2nd

Author(s)
James Stewart

Pages
830 pages

ISBN
9781133112280

**Sketch the graph of a function that is continuous on (1, 5) and has the given properties.**

** **

**8. Absolute minimum at 1, absolute maximum at 5, local maximum at 2, local minimum at 4.**

The graph is sketched.

The given function is the value of absolute minimum is at 1, absolute maximum is at 5, local maximum at 2, local minimum at 4.

** ****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.**

To keep it simple, I will use straight line segments to draw the graph. It is not given that \(f\) is differentiable everywhere, so its graph need not be smooth at all points. Note that: If the absolute minimum/maximum are not the endpoints of the domain and the function is continuous (as the case here), they are also the local minimum/maximum, respectively.

It is not necessary to draw the dashed vertical lines at \(x = 1,5\). I am drawing them to show that the function is defined between (and on the) two boundaries. The graph of the given function is:

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