JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 29)
Let $$f(x)=2^x-x^2, x \in \mathbb{R}$$. If $$m$$ and $$n$$ are respectively the number of points at which the curves $$y=f(x)$$ and $$y=f^{\prime}(x)$$ intersect the $$x$$-axis, then the value of $$\mathrm{m}+\mathrm{n}$$ is ___________.
Answer
5
Explanation
_29th_January_Morning_Shift_en_29_1.png)
$$\begin{aligned} & \therefore \mathrm{m}=3 \\ & \mathrm{f}^{\prime}(\mathrm{x})=2^{\mathrm{x}} \ln 2-2 \mathrm{x}=0 \\ & 2^{\mathrm{x}} \ln 2=2 \mathrm{x} \end{aligned}$$
_29th_January_Morning_Shift_en_29_2.png)
$$\begin{aligned} & \therefore \mathrm{n}=2 \\ & \Rightarrow \mathrm{m}+\mathrm{n}=5 \end{aligned}$$
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