= Solution
The <sine addition formula> gives $(\sin x+\cos x)/\sqrt2=\sin(x+\pi/4)$. On the requested <interval> the shifted angle runs from $0$ to $\pi/2$, so the graph rises from $(-\pi/4,0)$ through $(0,1/\sqrt2)$ to $(\pi/4,1)$.
Its <derivative> $\cos(x+\pi/4)$ is nonnegative and reaches zero only at the right endpoint. Its second <derivative> is $-\sin(x+\pi/4)\leq0$, so the rising arc is concave downward and ends with a horizontal tangent.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1-shifted-sine.png]
{title=A rising concave-down quarter sine wave on the specified interval}
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