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Tushar Watts Grade: 12

Let S be the set of real values of parameter k for which te eqn f(x) = 2x 3 - 3(2+k)x 2 +12kx has exactly one local minimum and exactly one local maximum.  S is a subset of

(a) (-4, ∞)      (b) (-3,3)        (c) (3,∞)   (d)  (- ∞,0

8 years ago

Answers : (1)

Ramesh V
70 Points

f '(x) = 6(x2 - x(2+k) +2k ) =0

so roots of f '(x) are 2,k

f "(x) = 6( 2x -(2+k))

to have one local minima ( f "(x) > 0 )and local maxima ( f "(x) < 0 )

so , its k > 2 which is subset of (-4, infinity)

option A


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Naga Ramesh

IIT Kgp - 2005 batch



8 years ago
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