Let f(x) = int e^x (x - 1)(x - 2) dx. In whic | vedclass

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(B) function $f(x)$ is decreasing when its derivative $f'(x) < 0$. Given $f(x) = \int e^x (x - 1)(x - 2) dx$. By the Fundamental Theorem of Calculus,t

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$(1, 2)$

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(B) function $f(x)$ is decreasing when its derivative $f'(x) Given $f(x) = \int e^x (x - 1)(x - 2) dx$. By the Fundamental Theorem of Calculus,the derivative is $f'(x) = e^x (x - 1)(x - 2)$. Since $e^x$ is always positive for all real $x$,the sign of $f'(x)$ depends on the product $(x - 1)(x - 2)$. We set $f'(x) This inequality holds when $x$ lies between the roots $1$ and $2$. Therefore,$f(x)$ is a decreasing function in the interval $(1, 2)$.

Let $f(x) = \int e^x (x - 1)(x - 2) dx$. In which interval is $f$ a decreasing function?

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