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Mariana [72]
3 years ago
14

Let f be a continuous function on the closed interval [ − 2 , 5 ]. If f((-2)=-7 and f(5)=1, then the Intermediate Value Theorem

guarantees that
Mathematics
1 answer:
azamat3 years ago
6 0

Answer:

The function has at least 1 zero within the interval [-2,5].

Step-by-step explanation:

The intermediate value theorem states that, for a function continuous in a certain interval [a,b], then the function takes any value between f(a) and f(b) at some point within that interval.

This theorem has an important consequence:

If a function f(x) is continuous in an interval [a,b], and the sign of the function changes at the extreme points of the interval:

f(a)>0\\f(b) (or viceversa)

Then the function f(x) has at least one zero within the interval [a,b].

We can apply the theorem to this case. In fact, here we have a function f(x) continuous within the interval

[-2,5]

And we also know that the function changes sign at the extreme points of the interval:

f(-2)=-70

Therefore, the function has at least 1 zero within the interval [-2,5], so there is at least one point x' within this interval such that

f(x')=0

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Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the
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Answer:

1. The volume of the pile is 4,399.7719 m^3

2. The number of sanders to be filled from a pile is 638

Step-by-step explanation:

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V = 1/3 * pi * r^2 * h

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r = 34.4/2 = 17.2 m

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To find the number of sanders to be filled,

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There is a population of 15,500 bacteria in a colony. If the number of bacteria doubles every 234 hours, what will
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Answer:

2,48,000

Step-by-step explanation:

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  • After 234 hours, no. of bacteria = 2(15,500) = 31,000

  • After 468 hours, no. of bacteria = 2(31,000) = 62,000 (2*234 = 468)

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