Science:Math Exam Resources/Courses/MATH100/December 2018/Question 05 (d)/Solution 1

We know from part (c) that $f^{″}(x)$ changes sign at $x=5/2$, and we have $f(5/2)=(5/2{)}^{9/7}+(9/2)(5/2{)}^{2/7}=7\cdot (5/2{)}^{2/7}$. Therefore, the only inflection point is at $(x,y)=(5/2,7\cdot (5/2{)}^{2/7})$.