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Tanya [424]
3 years ago
13

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

e f(c)=0
Mathematics
1 answer:
iragen [17]3 years ago
7 0

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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Tentukan mean, median, dan modus dari 7,4,5,6,7,4,5,7,8,9, dan 6
Anvisha [2.4K]

Answer:

<h3>Median = 6</h3><h3>Mean = 6,1</h3><h3>Modus = 7</h3>

Step-by-step explanation:

Median (Nila tengah setelah data diurutkan)

= 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 9

= 6

Mean

= jumlah data / banyak data

= 4+4+5+5+6+6+7+7+7+8+9/11

= 68/11

= 6,1

Modus

= data yang paling banyak muncul

= 7 (muncul sebanyak 3 kali)

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3 years ago
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Svetlanka [38]

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3 0
2 years ago
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We need the graph!!!!!!!
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Answer:

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Step-by-step explanation:

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