Let f(x)=2 x -x 2 , x in R . If m and n are respectively the number of points at which the curves y = f ( x ) and y = f prime ( x ) intersects the x -axis, then the value of m+n is

Mathematics · Application of Derivatives

JEE Main 2024 — 29 January, Shift 1 — Question 23

Let $f(x)=2^{x}-x^{2}, x \in R$ . If $m$ and $n$ are respectively the number of points at which the curves $\mathrm{y}=\mathrm{f}(\mathrm{x})$ and $\mathrm{y}=\mathrm{f}^{\prime}(\mathrm{x})$ intersects the x -axis, then the value of $m+n$ is

Answer: 5

Numerical answer — enter this value.

Step-by-step solution

$\therefore \mathrm{m}=3$

$f^{\prime}(x)=2^{x} \ln 2-2 x=0$

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

$\therefore \mathrm{n}=2$

$\Rightarrow \mathrm{m}+\mathrm{n}=5$

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Mathematics
Chapter: Application of Derivatives
Topic: Monotonicity

Consider the function f: [1/2, 1 ] arrow R defined by f(x)=4 √(2) x^3-3 √(2) x-1 . Consider the statements (I) The curve y=f(x) intersects…

Answer: 5

Step-by-step solution

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