Question
Let R denote the set of all real numbers. Let f: R R be defined by f(x)= cases 6 x+ x 2 x+ x & if x 0 \\ 7 3 & if x=0 cases Then which of the following statements is (are) TRUE?
JEE Advanced
Mathematics
Application of Derivatives
2025
JEE Advanced 2025 (Paper 2)
JEE Advanced Mathematics Question (2025) — Solution
Options
- A. The point x=0 is a point of local maxima of f
- B. The point x=0 is a point of local minima of f
- C. Number of points of local maxima of f in the interval [ , 6 ] is 3
- D. Number of points of local minima of f in the interval [2 , 4 ] is 1
Answer
D. Number of points of local minima of f in the interval [2 , 4 ] is 1
Step-by-step solution
since 3> 7 3 3>f(0) x=0 is local minima ....option (B) is correct Now, aligned & f(x)= 6 x+ x 2 x+ x =1+ 4 x 2 x+ x \\ & f^ (x)= 4[(2 x+ x) 1-x(2+ x)] (2 x+ x)^2 = 4( x-x x) (2 x+ x)^2 \\ & = 4 x( x-x) (2 x+ x)^2 aligned Options (C) \& (D) are also correct.
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