Question

If you have a graphing calculator or computer, why do you need calculus to graph a function?

Short answer

If we want to draw a very accurate graph of the work, we can use Calculus to do so. We can determine the background, intercepts, and asymptotes from the actual work. Then, if the function is subdivided into intervals, then we can also determine its interval.

Step-by-step solution

Calculus-based curve drawing

If we want to draw a very accurate graph of the work, we can use Calculus to do so. We can determine the background, intercepts, and asymptotes from the actual work. Then, if the function is subdivided, we can determine the intervals when the function ascends or descends, as well as the location of any extrema. Finally, if the task is split in two, we can determine when the task is curved upward or downward, as well as the location of any variable points.

Response and Justification

always have a calculator in your pocket." Yes, this is no longer true. With smartphones constantly attached to us, we can get a graph of any activity. However, the graph we are building will always be more informative than the graph we have just received for the following reasons.

i. We may incorrectly type the activity on our computer or calculator, which will lead to an incorrect graph. Since this is a mistake, we will not be aware that we have written it wrong, and we may come to the wrong conclusions.

ii. Some tasks have behaviors that are very difficult to see in the graph. Depending on how we measure our axes, we may miss out on extrema. Consider the work that can be done at a minimum and the size associated with it. If our y-axis is measured from 100 to 100, the curve may appear horizontal between these points, as the decrease is very small. Therefore, we can completely miss these two situations.

iii. Some features of the graph of functions in strange ways that can be misleading. For example, some calculators try to force a continuation even on non-continuous objects. This means that if a team member has a straightforward asymptote, a graphing calculator may draw a straight line between work breaks. This may make us think that the work is going on if it is not. Another situation is when the graph rotates very fast but we are not close enough to see it. In this case, we may see a dark pattern on our graph, as the points are too close to separate.