SAT1000 - P320

Given the function $f(x)= \sin(\omega x+\phi)\ (\omega>0, |\phi| \leq \dfrac{\pi}{2})$ , $f(-\dfrac{\pi}{4})=0, f'(\dfrac{\pi}{4})=0$ , and $f(x)$ is strictly monotone on the interval $(\dfrac{\pi}{18}, \dfrac{5\pi}{36})$ , then find the maximum value of $\omega$ .

Have a look at my problem set: SAT 1000 problems