Use the intermediate value theorem to show that there is a root of the given equation in the specified interval. x^4+x-9=0, (1,2)

Answer 1

When x = 1, the function evaluates to 1 + 1 - 9 = -7 < 0

When x = 2, evaluates to 16 + 2 - 9 = 9 > 0

The function is a polynomial so is continuous

Therefore by the intermediate value theorem as f(1) < 0 and f(2) > 0 and f is continuous there must be at least one value of x in (1,2) where f(x) = 0

Mike