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Kisachek [45]
3 years ago
12

What is the probability that the individual purchased a small cup? a cup of decaf coffee?

Mathematics
1 answer:
guapka [62]3 years ago
8 0
30% sjisizhzbs sjaisiBzbs shauauabasbsbshhasbshjasnbssjusshbssususbshsns
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if f is a differentiable function and f(0)=-1 and f(4)-3 then which of the following must be true there exists a c in [0,4] wher
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Answer:

True, see proof below.

Step-by-step explanation:

Remember two theorems about continuity:

  1. If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.
  2. (Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.

If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.

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What is the domain and range?
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Answer:

Domain: {-6, -2, -1, 1, 3, 6}

Range: {-6, -2, -1, 0, 3}

Step-by-step explanation:

to find the domain of a function, you look at all the possible x-values. this means you look at all the points, and see what their x-values are.

for example, the first point on the left is at (-6, -1). this means that -6 is in the domain. continue doing this for all the points, and you get {-6, -2, -1, 1, 3, 6}

to find the range of a function, it's just like domain but with y-values.

for example, for the leftmost point, it's at (-6, -1) so -1 is part of the range. continuing this with all the points, you get {-6, -2, -1, 0, 3}

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Step-by-step explanation:

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