Mathematics - Application of Derivative Question with Solution | TestHub
MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB
MathematicsMediummatching list
For the function : Column – I
(A) has a local maximum at
(B) has a local minimum at
(C) has a local extremum at
(D) is not differentiable at
Column – II
(p) When ,
(q) When ,
(r) When ,
(s) When ,
Options:
Answer:
A
Solution:
f(x) = ax^2 - b|x| is even; for x >= 0, f(x) = ax^2 - bx and f′(x) = 2ax - b. (A) Near x = 0, f(x) - f(0) ~ -b|x| < 0 iff b > 0, so x = 0 is a local maximum when b > 0: (p), (s). (B) x = 0 is a local minimum iff b < 0: (q), (r). (C) For x > 0, f′(x) = 0 at x = b/2a, valid when a, b have the same sign: (p), (r). (D) |x| is not differentiable at 0, so f is not differentiable at x = 0 in all cases: (p), (q), (r), (s). Hence option A.
Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima
⏱ 2mℹ️ Source: QB
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