Question

How do you find the solution to this problem? Explain step by step please.

Answer 1

We can compute the values of the function at the end-points:

`f(-2) = 6(-2)^4 + 9(-2)^3 - 5(-2) - 8`

`f(-2) = 6(16) + 9(-8) + 10 - 8`

`f(-2) =26`

Now for `x =-1`:

`f(-1) = 6(-1)^4 + 9(-1)^3 - 5(-1) - 8`

`f(-1) = 6- 9 + 5 - 8`

`f(-1) = -6`

Since polynomial functions are continuous everywhere on their domain, there must be a point `x= c` such that `f(c) = 0`, because for the function to get from `y = 26` to `y = -6` it must cross the x-axis somewhere on the interval `[-2, -1]`.

Therefore, there will be an x-intercept on `[-2, -1]`.

Hopefully this helps!