3.62: Curve from second derivative; nature; exponential rates

A curve $y = f(x)$ satisfies $f''(x) = (2x + 5)^{-\frac{3}{2}}$. The curve has gradient $\dfrac{3}{2}$ at $(2,\ 2)$. Find the coordinates of the stationary point on the curve.

Determine the nature of this stationary point.