## Calculus with Applications (10th Edition)

$$f(x)=18x-18e^{-x}$$ $f(x)$ is never concave upward $f(x)$ always concave downward No Inflection points.
$$f(x)=18x-18e^{-x}$$ The first derivative is \begin{aligned} f^{\prime}(x) &=18-(-1)18e^{-x}\\ &=18+18e^{-x} , \end{aligned} and the second derivative is \begin{aligned} f^{\prime\prime}(x) &=0+18(-1)e^{-x} ,\\ &=-18e^{-x} \end{aligned} Since \begin{aligned} f^{\prime\prime}(x) &=-18e^{-x} \lt 0 \end{aligned} for all $x$, so function $f$ is always concave downward and never concave upward and also there are no points of inflection .