To warm yourselves up for the graphing assignment,click on the link below. It is an applet where you can practice graphing derivatives from the graphs of functions. Don't rush through it. Take the time to jot down your thoughts before you check your answer. After using the applet for at least 10 functions, answer the following questions.
Don't forget to use the uphill/downhill analysis, bowl analysis, and shape predictions !!
1.) On the graph of a derivative, we see zeroes (on the x-axis) where the original graph has a max or min. You will see some zeroes in this applet that do not represent max or min. What do you think they represent? How can you tell the difference between the "max-min zeroes" and these impostors??
2.) Remember "bowl up" or "bowl down"? That is technically called concavity. When a graph is "bowl up" or concave up, its derivative graph will always be going in which direction? Is the inverse of that true?
3.) In your own words, describe where points of inflection occur on the original graph. What are the ways to show a point of inflection on a derivative graph? (Hint: See problem 1.)
Derivative Graphs - Practice Applet
1. I think they represent thing seen in such like jump discontinuities joined by horizontal lines, being slopes = 0. You can tell those kinds of things apart from the max/min ones by identifying the change in the direction of the curve, like the peak of the hills on the graph.
ReplyDelete2. It will always be going up-right, looking like the line y=x. The inverse of the bowl f(x), like y=sqrt(x), isn't necessarily true because it isn't continuous.
3. Points of inflection occur at parts where the output changes from one sign to another (+ to - and vice versa). You can tell those ones apart by seeing if they hit the 0s of the derivative graph.
BTW, that was Michael Ferrer
ReplyDelete1. The zeroes occur when there is a point of discontinuity in the graph, such as a hole or a horizontal asymptote. To tell them apart from other zeroes you would need to pair them with the original function.
ReplyDelete2. If the function is bowl up, the derivative will be going in the positive direction, and the inverse is true.
3. Points of inflection occur when the graph changes sign. You can tell where they are when there is a bowl up or down.
1. The zeroes happen when there is some sort of discontinuity, whether it be jump or otherwise. the bast way to tell them apart is to compare them with the original graph.
ReplyDelete2. if the concave, or bowl is up, then the line will be moving up and right. the opposite is true
3. points of inflection occure when the graph changes from moving up tp down, or vice versa. the b est way to mark them is by marking the bowls
1. The zeroes that do not represent max or min represent points of discontinuity in the derivative. Max/min zeroes can be identified by the change of direction in a curve.
ReplyDelete2. When the graph is "bowl up", the derivative will be going in a positive direction. The inverse of that is true.
3. The points of inflection occur when the graph changes sign or at the max and min points.
1. Zeros appear when there is discontinuity in the graph. To tell them apart, compare with the original function.
ReplyDelete2. If the graph is bowl up, then the derivative will move positively; if bowl down, then derivative moves negatively.
3. Points of inflection are where the graph changes sign, or at max/min points
1. I think that those zeros are discontinuities in the graph. The real max/min zeros occur at change of direction in the original graph.
ReplyDelete2. It will be moving up and right. The inverse is true.
3. Points of infliction are when the graph changes from moving down to up or up to down. When the it bowls up or down
1. The zeroes are where there is discontinuity in the graph. To find the real max/mins, you have to look at original graph and see where there is a change of direction in the graph.
ReplyDelete2. When the graph is "bowl up" , the derivative will be moving up and right. The inverse is true.
3.The point of inflection is where the graph changes signs. As you said in class, it is at the one point of a downslope/upslope graph where it is at the steepest point. You can tell where they are by the bowl up or bowl down.
1. the zeros on the graph are discontiuities. To find the max or min you need to look at the original function.
ReplyDelete2.If the derivitive is bowl up that means the original function has a positive slope same with the inverse but a negitive slope.
3.Points of inflection is where on the original function the graph turns around and heads in the opposite direction. This happens at the min and max of the funcion.