Let \( \mathrm{f} \), \( \mathrm{g}:[-1,2] \rightarrow \mathrm{R} \) be continuous functions which are twice differentiable on the interval \( (-1,2) \). Let the values of \( f \) and \( g \) at the points \( -1,0 \) and 2 be as given in the following table:
math xmlns=http://www.w3.org/1998/Math/MathMLmtable rowlines=solid columnlines=solid frame=solidmtrmtd/mtdmtdmix/mimo=/momo-/momn1/mn/mtdmtdmix/mimo=/momn0/mn/mtdmtdmix/mimo=/momn2/mn/mtd/mtrmtrmtdmif/mimo(/momix/mimo)/mo/mtdmtdmn3/mn/mtdmtdmn6/mn/mtdmtdmn0/mn/mtd/mtrmtrmtdmig/mimo(/momix/mimo)/mo/mtdmtdmn0/mn/mtdmtdmn1/mn/mtdmtdmo-/momn1/mn/mtd/mtr/mtable/math
In each of the intervals \( (-1,0) \) and \( (0,2) \) the function \( (f-3 g)^{\prime \prime} \) never vanishes. Then the correct statement(s) is(are)
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