Question

The following table gives a partial set of values of a polynomial function.

x –2 –1 0 1 2 3
g(x) –14 –2 0 –4 –6 2

Between which two values would a relative maximum most likely occur?
–2 and 0
–1 and 1
0 and 2
1 and 3

Answer 1

The values of x between which the relative maximum occurs is between the x-values; -1 and 1

The known parameters;

The table of the partial set of the polynomial values is presented as follows;

$\begin{array}{rcr}\mathbf{x}&&\mathbf{g(x)}\\-2&&-14\\-1&&-2\\0&&0\\1&&-4\\2&&-6\\3&&2\end{array}$

From the table above, we have that g(x) is maximum (g(x) = 2) when x = 3

Method;

Define and find the relative maximum

The relative maximum of a function, is given by a point where the graph of the function changes direction from 'continuously' increasing values of the function before the point to 'continuously' decreasing values of the function after the point

From the table, at x = -2, -1, 0, g(x) = -14, -2, 0, and is therefore, increasing

Where, x = 0, 1, 2, we have g(x) = 0, -4, -6, therefore, g(x) is decreasing

The maximum value of g(x), in the region where g(x) changes from increasing to decreasing is g(x) = 0, which is given between the x-values of -1 and 1

Therefore, the relative maximum is most likely to occur between the values of x = -1, and x = 1, which is the option -1 and 1

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