The function $f(x)$ passes through the point $(-1,6)$ and $f'(x)=3x^2+2x+1$

Question

a) find $f(x)$

I found that to be $f(x) = x^3+x^2+x+7$

b) Prove $f$ has a root between $x=-3$ and $x=-2$

I don't know how to do part b.

Answer 1

Hint: Use the Intermediate Value Theorem.