examday

/TMUA

$f(x)=\sin(ax+b)$, where $a>0$ and $|b|\le\frac\pi2$. $x=-\frac\pi4$ is a zero of $f(x)$, and $f(x)\le\left|f\left(\frac\pi4\right)\right|$ for all $x$. If there is a minimum but no maximum in the interval $\left(-\frac\pi{12},\frac\pi{24}\right)$, then the maximum value of $a$ is