Methods 12 Part 1

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to be a quartic the highest degree of the polynomial must be 4, but what exactly constitutes a `W-shaped quartic'.
A `W-shaped quartic' has two distant inflection points. For example, the two inflection points were Q and R as seen in Figure 1. For it to be a quartic however, we can draw a line between the two-inflection points Q and R. If a straight line is drawn between those two lines, for it to be a `W-shaped quartic' it must hit the graph at two more points, which we can call P and S. The graph must also be symmetrical for it to be a `W-shaped quartic'.
There were more assumptions for each individual task which should be stated at the top of the task before I show my working out.
My method outline was:
Finish constructing lines based on the equation given.
Solve the ratios of areas in Task 1
Use desmos to monitor and generalize findings for Task 2 and 3 and then apply mathematical techniques to see if findings were correct.
Solve the ratio in Task 4
Application of ...

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to get the expression 12x2-36x, then just simply equate that to O for which the classpad will solve the answer. Then we can do the same steps of substituting the x-value back into the original equation, or simply defining the original function using the keyboard and then solving.


One thing we must keep in mind when doing this is that the double derivative being equal to 0 doesn't automatically make a point of point of inflection. Another feature of a point of inflection is that it is the point at which the graph usually changes concavity (i.e., from being concave up to concave down and vice versa). In order to look for this a sign test must be conducted using an x-value to the left or ...

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