Science:Math Exam Resources/Courses/MATH104/December 2016/Question 02 (b)/Solution 1

The first derivative of m is straightforward, if the derivative is positive, then $f^{'} > 0$ .

For $f^{″}$ , we use the points of inflection (3 and 5 from question). 3 is one inflection point. From 0 to 3, $f^{'}$ goes from positive to negative, thus during that area, $f^{″} < 0$ . For $t \in [3, 5], f^{″} > 0$ . For $t > 5, f^{″} < 0$ .

The part where $f^{'}, f^{″}$ are both positive: $(4, 5)$

The part where $f^{'}, f^{″}$ are both negative: $(2, 3)$

answer: $(2, 3), (4, 5)$