Question

Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 4x 2, [0, 9], f(c) = 23 c =

Answer 1

The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.

Especially, he has been credited with proving the following five theorems:  a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same;  the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.

In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.

In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a  theorem and is maximum extensively used in the domain of science.

2-1

and interval = [4]

since, function fext is continuous in ginen

interval. And also

+(4) = 42+4

4-1

=

20 = 6667

$(5/4) = ($145/2

stone-1

= 5.833

simle, f(4) > $(5/2), hence Intermediate

Theorem & applies to the indicated

proved.

Now,

= 6

C-1

C-5c +6 = 0

C=2 or c=3

1=

3 or

C= 2, 3

<= 2

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