Chapter 4.1, Problem 1E

To determine

Calculate the absolute maximum, absolute minimum and extrema of f, by using the graph.

Answer to Problem 1E

The absolute maximum is = $4$ at $x=2$ .

The absolute minimum is = $0$ at $x=4$ .

The local extrema = does not exist.

Explanation of Solution

Given :

It is given in the question that the graph is given below:

  

Concept Used:

In this we have to use the concept of the application of derivatives.

Calculation:

By observing the graph we get

  $x\in \left[1,11\right]$ & $y\in \left[0,4\right]$

Since,

  $\text{Y}=\text{f}\left(\text{x}\right)$

  $\text{f}\left(\text{2}\right)=\text{4}$ (which is absolute maximum)

  $\text{f}\left(\text{4}\right)=0$ (which is absolute minimum)

we find the local minima and local maxima,

as we know that the derivative of a constant function is $0$ . In this question there is no extrema of f.

Conclusion:

The absolute maximum is = $4$ at $x=2$ .

The absolute minimum is = $0$ at $x=4$ .

The local extrema = does not exist.