Question

Sketch the graph of \(f\) by hand and use your sketch to find the absolute and local maximum and minimum values of \(f\). (Use the graphs and transformations of Sections 1.2.)

21. \(f(x) = 1 - \sqrt x \)

Short answer

The absolute maximum occurs at \(x = 0\). There is no absolute minimum as well as the local extrema.

Step-by-step solution

Given data

The given function is \(f(x) = 1 - \sqrt x \).

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 of the function

Let \(y = f(x)\).

Obtain the values of \(y\) for various values of \(x\) as shown in below table and draw the graph of \(f(x)\) as shown below in Figure 1.

From Figure 1, it is observed that there is no absolute minimum and local extrema as the curve approaches numerically large values.

Notice that the only highest point of the curve occurs at \(x = 0\). Therefore, the absolute maximum value is \(f(0) = 1\).