Chapter 4, Problem 36RE

(a)

To determine

To Find: The absolute extrema of function.

Answer to Problem 36RE

The absolute minimum value is $-2$ at $x=1$ and the absolute maximum value is $3$ at $x=3$ .

Explanation of Solution

Given:

The function is continuous on $\left[0,3\right]$

Calculation:

From the given data, it is clear that the function is decreasing on $\left[0,1\right]$ and increasing on $\left[1,3\right]$ . The absolute minima is at $x=1$ and the absolute maxima is at end points. Now,

  $\begin{array}{l}f(0)=0\\ f(1)=-2\\ f(3)=3\end{array}$

So, the absolute minimum value is $-2$ at $x=1$ and the absolute maximum value is $3$ at $x=3$ .

Conclusion:

The absolute minimum value is $-2$ at $x=1$ and the absolute maximum value is $3$ at $x=3$ .

(b)

To determine

The point of inflection.

Answer to Problem 36RE

There is no point of inflection.

Explanation of Solution

Given:

The function is continuous on $\left[0,3\right]$

Calculation:

There is no change in concavity. Hence, no inflection point is there in the graph.

Conclusion:

There is no point of inflection.

(c)

To determine

Draw the graph of function.

Answer to Problem 36RE

The graph of the function is drawn.

Explanation of Solution

Given:

The function is continuous on $\left[0,3\right]$

Calculation:

The graph of the function is:

As, the function has the absolute minimum value is $-2$ at $x=1$ and the absolute maximum value is $3$ at $x=3$ .

Therefore, the graph can be plotted with the points such as:

x	y
0	0
1	-2
3	3

  

Conclusion:

The graph of the function is drawn.