Science:Math Exam Resources/Courses/MATH102/December 2016/Question A 06/Solution 1

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At the points where has a min/max (slope of tangent line =0), must be equal to zero, i.e. intersects x-axis. This fact eliminates the option of , because if so, we then see that at its maximum point neither nor vanishes.


Now we have two choices, for each of which we check whether the graphs match:

  • If , we see that at 's max and min, intersects x-axis, this means that so we must have which implies that where has a max or min must become zero, however, we've already seen that at 's maximum is NOT zero. .


  • If , we see that at 's max and min, intersects x-axis, this means that so we must have which implies that where has a max or min must become zero, which we see that it is in fact true.


Therefore, the correct choice is , , and .

Answer: