In which of the following intervals does f(x) | vedclass

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(A) We want to find the interval where $f(x)$ increases less rapidly than $g(x)$,which means $f'(x) < g'(x)$.Let $h(x) = g(x) - f(x) = -2x^3 + 9x^2 -

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$(1, 2)$

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(A) We want to find the interval where $f(x)$ increases less rapidly than $g(x)$,which means $f'(x) Let $h(x) = g(x) - f(x) = -2x^3 + 9x^2 - 12x + 6$.We want $h'(x) > 0$ for $f(x)$ to increase less rapidly than $g(x)$.$h'(x) = -6x^2 + 18x - 12 = -6(x^2 - 3x + 2) = -6(x - 1)(x - 2)$.For $h'(x) > 0$,we need $(x - 1)(x - 2) This inequality holds when $x \in (1, 2)$.Thus,in the interval $(1, 2)$,$f(x)$ increases less rapidly than $g(x)$.

In which of the following intervals does $f(x) = 2x^3$ increase less rapidly than $g(x) = 9x^2 - 12x + 6$?

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