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The calling structure is shown in the following. For each class, the functions of that class are listed and then for each function that calls other functions, those called functions are listed. For MM testing, every one of those calls must be executed. For example, four calls to point will be made. No decisions are shown; however, in this program, there are no decisions that affect the calling sequence. class point point() getx() gety() class rectangle rectangle() point::point() point::point() point::point() point::point() length() point::getx() point::getx() point::gety() point::gety() area() length() length() class linklistnode linklistnode() getNext() getRectangle() setnext() class rectanglelist rectanglelist() addRectangle() rectangle::rectangle() linklistnode::linklistnode() linklistnode::setnext() totalArea() linklistnode::getRectangle() rectangle::area() linklistnode::getNext() MM testing: Any test case that builds at least one rectangle and then gets the total area will execute all of these calls.

8.14 Find the value(s) of c guaranteed by Rolle s Theorem for the function f(x) = 4x + 39x2 46 x 3 + 17 x 4 2 x 5 on the interval [0, 4].

When you first start YouTube, you usually see the Featured videos on YouTube that day. Just scroll through the video choices as you do in other apps.

Since f(x) is a polynomial, it is continuous and differentiable everywhere. First we verify that f(0) = f(4) = 0. f[x_]= 4 x + 39 x 2 46 x 3 + 17 x 4 2 x 5; f[0] 0 f[4] 0 Now we look to see where f '(c) = 0. Since f ' is a polynomial, we can use NSolve. NSolve[f'[c] 0]

0.0472411}, {c 1.05962}, {c 2.27466}, {c 3.51296}}

Along the bottom of the YouTube app are seven icons; Featured, Top Rated, Most Viewed, Favorites, Subscriptions, My videos, and History. Each is fairly selfexplanatory.

Function pair coverage requires that for all possible sequences of method executions, those of length two must be tested. This is usually done based on a state machine diagram or on a regular expression showing the possible method executions.

There are three values of c between 0 and 4 (Rolle s Theorem guarantees at least one). A plot of the graph confirms our result. Plot[f[x], {x, 1, 4}]

8.15 Verify the Mean Value Theorem for the function f ( x ) = x + sin 2 x on the interval [0, ].

To see the videos that YouTube is featuring that day, just touch the Featured icon. To see those videos that are most-viewed online, just touch the Most Viewed icon. After you watch a particular video, you will have the option to set it as a favorite on YouTube for easy retrieval later on. If you have set bookmarks, they will appear when you touch the Favorite icon.

f (x) is continuous and differentiable everywhere. Define a = 0, b = and solve the equation f (b) f (a) = f ' (c)(b a) for c. To approximate their values, we look at the graph with the endpoints connected by a line segment. f[x_] = x + Sin[2 x] ; a = 0; b = o; m = f[b] f[a]; b a l[x_] = f[a]+ m (x a);

Since a regular expression can be mapped to a nite state machine, these two approaches are equivalent. Although the nite state machine used to describe the behavior of a software system may not be minimal, having additional states will increase the e ectiveness of the test set.

Plot[{f[x], l[x]}, {x, a, b}]

You can search the huge library of YouTube videos. Touch the search box as in previous apps, and the keyboard will pop up. Type in a phrase, topic, or even the name of a video. In this example, I am looking for the newest Made Simple Learning video tutorial so I just type in Made Simple Learning and I see the list of videos to watch. When I find the video I want to watch, I can touch on it to see more information. I can even rate the video by touching on the video during playback and selecting a rating.

3.0 2.5 2.0 1.5 1.0 0.5 0.5 1.0 1.5 2.0 2.5 3.0

It looks like the tangent line will be parallel to the secant when x 1 or x 2.5. Clearly both values lie between 0 and . FindRoot[f[b] f[a] f'[c](b a), {c, 1}] FindRoot[f[b] f[a] f'[c](b a), {c, 2.5}]