Chapter 1.7, Problem 85PPE

To determine

To identify the function as linear or non-linear, estimate and interpret the intercepts of graph.

Explanation of Solution

Given:

  

Here, x - axis represents Number of Widgets

y - axis represents Average Cost per Widget ($)

When the graph is interpreted, it is clear that the graph is a parabola and as the Number of Widgets increases, the average Cost per widget first decreases, then attains minimum value and then keeps on increasing.

Here, the rate of change of Average Cost per Widget depends upon change in Number of Widget. Hence the function is non-linear.

The curve is above the x-axis for the entire domain. Hence, the function is positive.

The y-intercept is (0, 60). It means that, when the Numbers of Widgets is 0, average Cost per unit Widget will be 60 $. So, this point is a relative extrema.

While if the curve is further interpreted, it is visible that the graph obtains its minimum at the point (16, 10) which means, when the Number of Widgets is 16 the Avgerage Cost per Unit Widget is 10$ and this is the minimum value for the graph.

So, the Average Cost will not go below 10$.

Also, it is clear that, the line $x=16$ is the line of symmetry for the curve.