A signal is modelled by y = sin x + cos x for 0 ≤ x ≤ 2π, with x in radians…

Step 1. The derivative. $y' = \cos x - \sin x$.

Step 2. Flat tangents. $\cos x = \sin x$ means $\tan x = 1$. In $[0, 2\pi]$ the solutions are $x = \dfrac{\pi}{4} \approx 0.785$ and $x = \dfrac{5\pi}{4} \approx 3.927$.

Step 3. The heights. At $x = \dfrac{\pi}{4}$, $y = \dfrac{1}{\sqrt{2}} + \dfrac{1}{\sqrt{2}} = \sqrt{2} \approx 1.414$. At $x = \dfrac{5\pi}{4}$, $y = -\sqrt{2}$.