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Serjik [45]
2 years ago
12

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

Mathematics
1 answer:
Olin [163]2 years ago
5 0

Answer:

The correct option is  d

f(1) =  -5

f(2) =  11

The correct option is d

The correct option is  c

the correct option is  b

Step-by-step explanation:

The given equation is

     f(x) =  x^4 + x -7 =0

The give interval  is (1,2)

 

   Now differentiating the equation

        f'(x) =  4x^3 +7 > 0

Therefore the equation is  positive  at the given interval

       Now at x= 1

  f(1) =  (1)^4 + 1 -7 =-5

       Now at x= 2

  f(2) =  (2)^4 + 2 -7 =11

Now at  the interval (1,2)

      f(1) < 0 < f(2)

i.e

      -5 < 0 < 11

this tell us that there is a value z within 1,2 and

   f(z) =  0

Which implies that there is a root within (1,2) according to the intermediate value theorem

     

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