Mathematics - Application of Derivative Question with Solution | TestHub

Let $f(x)=e^x-1-x,g(x)=\log (1+x)-x$

$h(x)=\sin x-x,p(x)=\log x-x$ for $\mathrm{g}(\mathrm{x})=\log (1+\mathrm{x})-\mathrm{x}$ ${\mathrm{g}}^{\prime }(\mathrm{x})=\frac{1}{1+\mathrm{x}}-1=\frac{-\mathrm{x}}{1+\mathrm{x}}<0\forall \mathrm{x}\in (0,1)$

$\mathrm{g}(\mathrm{x})$ is decreasing when $0<\mathrm{x}<1$. $g(0)>g(x{)}_{-}\Rightarrow \log (1+x)<x$

Similarly it can be done for other functions.