Question

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

Answer 1

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