Let \( f(x)=e^{(p+1) x}-e^{x} \) for real number \( p0 \), then Let \( g(t)=\int_{t}^{t+1} f(x) ...

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Counter-Strike: Source
Game:
Counter-Strike: Source (2004)
Duration: 4:02
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Let \( f(x)=e^{(p+1) x}-e^{x} \) for real number \( p0 \), then
Let \( g(t)=\int_{t}^{t+1} f(x) e^{t-x} d x \). The value of \( t=t_{\rho} \), for which \( g(t) \) is minimum, is
(a) \( -\log _{e} \frac{\left(e^{p}-1\right)}{p} \)
(b) \( -\frac{1}{p} \log _{e}\left(\frac{e^{p}-1}{p}\right) \)
(c) \( -\frac{1}{p} \log _{e}\left(\frac{(p+1)\left(e^{p}-1\right)}{p}\right) \)
(d) \( -\log _{e}\left((p+1)\left(e^{p}-1\right)\right) \)
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