A landscape architect is designing a section of a path. The elevation h h\,h of the path (in meters) relative to a reference level is modeled by the function
h(x)=112x4+sinx+5 h(x) = \frac{1}{12}x^4 + \sin x + 5 h(x)=121x4+sinx+5for −π≤x≤π-\pi \le x \le \pi−π≤x≤π, where x x\,x represents the horizontal distance in meters from a marker.
Determine whether the curve with equation y=h(x)y = h(x)y=h(x) has a point of inflection at the point where x=0x = 0x=0. Fully justify your answer.
