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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

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

Grade:12

1 Answers

Ramesh V
70 Points
14 years ago

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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