Question

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.

Short answer

The graph is sketched.

Step-by-step solution

Given data

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.

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.

Sketch the graph

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: