  We discuss the critical points of modular forms, or more generally the zeros
of quasimodular forms of depth $1$ for $\mathrm{PSL}_2(\mathbb Z)$. In
particular, we consider the derivatives of the unique weight $k$ modular forms
$f_k$ with the maximal number of consecutive zero Fourier coefficients
following the constant $1$. Our main results state that (1) every zero of a
depth $1$ quasimodular form near the derivative of the Eisenstein series in the
standard fundamental domain lies on the geodesic segment $\{z \in \mathbb H:
\Re(z)=1/2\}$, and (2) more than half of zeros of $f_k$ in the standard
fundamental domain lie on the geodesic segment $\{z \in \mathbb H:
\Re(z)=1/2\}$ for large enough $k$ with $k\equiv 0 \pmod{12}$.
