Use the intermediate value theorem to determine whether the polynomial function `f(x)=4x^4+10x^3+4x+5` has a zero on [-3,-2].
The intermediate value theorem states that if a function is continuous on an interval [a,b], and f(a)<k<f(b) or f(a)>k>f(b), then there exists at least one c in [a,b] such that f(c)=k.
(1) Polynomials are continuous everywhere, so f(x) is continuous on [-3,-2].
Then since 47>0>-19, there exists a c in [-3,-2] such that f(c)=0.
Therefore f(x) has at least one zero in the interval.