Mathematics - Functions Question with Solution | TestHub

Given,

Function $\mathrm{f}\left(\mathrm{x}\right)=2^{\mathrm{x}}-{\mathrm{x}}^2, \mathrm{x}\in \mathrm{R}$

Now, plotting the diagram of $y=2^{\mathrm{x}} \& y={\mathrm{x}}^2$ we get,

Now, from above diagram total point of intersection are three

$\therefore \mathrm{m}=3$

Now, finding ${\mathrm{f}}^{\text{'}}\left(\mathrm{x}\right)=2^{\mathrm{x}}\ln 2-2\mathrm{x}=0$

$2^{\mathrm{x}}\ln 2=2\mathrm{x}$

Now, again plotting the diagram of $\mathrm{y}=2^{\mathrm{x}}\ln 2 \& \mathrm{y}=2\mathrm{x}$ we get,

So, from above diagram total point of intersection is two

$\therefore \mathrm{n}=2$

Hence, $\mathrm{m}+\mathrm{n}=5$