1. The problem is to understand and analyze the function $g(x) = (s+1)e^x$. 2. The function $g(x)$ is a product of a constant term $(s+1)$ and the exponential function $e^x$. 3. Important rules: - The exponential function $e^x$ is always positive and increases as $x$ increases. - Multiplying by $(s+1)$ scales the function vertically. 4. To analyze $g(x)$, note that: - If $s+1 > 0$, $g(x)$ is an increasing exponential function. - If $s+1 = 0$, $g(x) = 0$ for all $x$. - If $s+1 < 0$, $g(x)$ is a decreasing exponential function (negative values). 5. The function has no zeros unless $s+1=0$. 6. The derivative is $g'(x) = (s+1)e^x$, which has the same sign as $g(x)$. 7. Therefore, $g(x)$ has no extrema (no maxima or minima) because $e^x$ is always positive and $(s+1)$ is constant. Final answer: The function $g(x) = (s+1)e^x$ is an exponential function scaled by $(s+1)$ with no zeros or extrema unless $(s+1)=0$, in which case it is identically zero.