Geometrical Explanation of Intermediate Value Theorem

Q. Which of the following statements is/are true for the function $f\left(x\right)=x^{13}+7x^3-5x+1$

1. $f\left(x\right)$ has at least $1$ root (real) in $[0,1]$
2. $f^{\prime }\left(x\right)$ has at least $1$ root (real) in $R$
3. $f\left(x\right)$ has at most $1$ root (real) in $[0,1]$
4. $f^{\prime }\left(x\right)$ has at most $1$ real root in $R$