Verify Rolles theorem for the function `f(x)=x^2+2x-8,``x in [-4,2]`.

Explanation

`f(x) = x^(2)+2x-8, x in [-4,2]`
`f(x)` is a polynomial function.
` :. f(x)` is continous in [-4, 2] and differentiable in (-4, 2).
Now `f'(x) =2x+2`
`f(-4)==(-4)^(2)+2(-4)-8`
`=16-8-8=0`
and `f(2)=2^(2)+2(2)-8=4+4-8=0`
` :. f(-4)=f(2)`
Therefore, f(x) stisfies all conditions of Roll's theorem in [-4, 2].
Let `f'(c)=0`
`implies2c+2=0`
`impliesc= -1 in (-4,2)`
Hence, Rolle's theorem is verified.