Answer
$f(-6) = 185$
$f(0) = -1$
$f(2) = 65$
Work Step by Step
Applying theorem 1.5.9 twice, once on [-6,0] and [0,2] which states that
If f is continuous on [a, b], and if f (a) and f (b) are nonzero and
have opposite signs, then there is at least one solution of the equation f (x) = 0 in the
interval (a, b)
so
$f(-6) = (-6)^{4}+5(-6)^{3}+5(-6)-1 = 185$
$f(0) = (0)^{4}+5(0)^{3}+5(0)-1 = -1$
$f(2) = (2)^{4}+5(2)^{3}+5(2)-1 = 65$
