diff --git a/project.ptx b/project.ptx index eeab6f35db..4fc5d12980 100644 --- a/project.ptx +++ b/project.ptx @@ -1,10 +1,6 @@ - - - - + + + + + g(x) = \dfrac{\sin(x)}{e^x} - the quotient of e^x and \sin(x) + the quotient of \sin(x) and e^x h(x) = \sin(e^x) diff --git a/source/proteus/proteus-3-1.xml b/source/proteus/proteus-3-1.xml index 6f0190b5a5..249ee852a2 100644 --- a/source/proteus/proteus-3-1.xml +++ b/source/proteus/proteus-3-1.xml @@ -34,28 +34,4 @@ - - -

- In this section we'll learn about things called the First Derivative Test and the Second Derivative Test. It will be helpful before we begin to remind ourselves of a few facts about the relationship between a function and its first and second derivatives. -

-

- Match each of the cards on the left with every applicable property on the right. -

- - - f''(x) \gt 0 - f''(x) \lt 0 - f'(x) \gt 0 - f'(x) \lt 0 - - f(x) increasing - f(x) decreasing - f(x) concave down - f'(x) decreasing - f(x) concave up - f'(x) increasing - - - diff --git a/source/proteus/proteus-3-2.xml b/source/proteus/proteus-3-2.xml index 7a3d5e789c..cef9ddd61e 100644 --- a/source/proteus/proteus-3-2.xml +++ b/source/proteus/proteus-3-2.xml @@ -6,25 +6,30 @@

- Open a browser and point it to Desmos. Choose any function you like, perhaps \ln(x) or \sqrt{x} or \tan(x). In Desmos, enter f(x)= your chosen function. + In the Desmos window below, there is a graph of a function that you can experiment with:

- In each of the parts of this activity, we'll create a new function related to f(x) by applying a parameter, which we can control with a slider. Explore with the sliders and describe how changing the value of the parameter with the slider affects the graph of the new function. Pay particular attention to the location of any critical points or inflection points. -

+ +

  1. - In Desmos, enter g(x) = a f(x). Explore the effect of the value of a. + Estimate the location of the relative minimum. +

    +
    2. +
  2. +

    + Estimate the location of the inflection point.

  3. - In Desmos, enter h(x) = f(b x). Explore the effect of the value of b. + Play with the slider for a. What happens to the location of the relative minimum? of the inflection point?

  4. - In Desmos, enter k(x) = f(x) + c. Explore the effect of the value of c. + Play with the slider for b. What happens to the location of the relative minimum? of the inflection point?

diff --git a/source/proteus/proteus-3-4.xml b/source/proteus/proteus-3-4.xml index ff7257f0cb..1ab0cbcae0 100644 --- a/source/proteus/proteus-3-4.xml +++ b/source/proteus/proteus-3-4.xml @@ -5,7 +5,7 @@

- Suppose you are building a fence around a rectangular field, and the field needs to have an area of 9000 square meters. There are many different shapes of rectangles you could consider. + Suppose you are building a fence around a rectangular field, and the field needs to have an area of 9000 square meters. There are many rectangles of different dimensions that you could consider.

    @@ -16,17 +16,17 @@

  1. - Another option you have considered is to make the field more like the shape of a piece of notebook paper. Draw a picture of what the field would look like in this case; remember, it still needs to have an area of 9000 square meters. + Another option you have considered is to make the field look like a piece of notebook paper. Draw a picture of what the field would look like in this case, labeling the measurements of your shape. Remember, the field still needs to have an area of 9000 square meters.

  2. - Draw at least one more picture of a rectangular field that is a different shape than what you’ve drawn before and would still have an area of 9000 square meters. + Draw at least one more picture of a rectangular field that is different than what you’ve drawn before and would still have an area of 9000 square meters.

  3. - Which measurements of your three fields are different? Which measurements of your three fields are the same? + Which measurements are different among your three fields? Which measurements are the same?

  4. diff --git a/source/proteus/proteus-3-5.xml b/source/proteus/proteus-3-5.xml index 62f8adff8c..7855a7e1b6 100644 --- a/source/proteus/proteus-3-5.xml +++ b/source/proteus/proteus-3-5.xml @@ -16,12 +16,12 @@

  5. - Draw three different pictures of the water in the water tank at three different times: at 2am, at 8am, and at 12pm. + Draw what you imagine the water in the tanks would look like at 2am, at 8am, and at 11am.

  6. - Which measurements of the amount of water are different in your different pictures? Which measurements are the same? + Which measurements of the water are different among your different pictures? Which measurements are the same?