Let f be a differentiable function on R such that f ( 2 ) = 1 , f ′ ( 2 ) = 4 . Let lim x → 0 ( f ( 2 + x ) ) 3/ x = e α . Then the number of times the curve y = 4 x 3 − 4 x 2 − 4 ( α − 7 ) x − α me

Question

Let f be a differentiable function on R such that f ( 2 ) = 1 , f ′ ( 2 ) = 4 . Let lim x → 0 ​ ( f ( 2 + x ) ) 3/ x = e α . Then the number of times the curve y = 4 x 3 − 4 x 2 − 4 ( α − 7 ) x − α meets x -axis is :-

TestHub · Accepted Answer

​ x → 0 lim ​ ( f ( 2 + x ) ) x 3 ​ e x → 0 lim ​ x ( f ( 2 + x ) − 1 ) 3 ​ e 3 f ′ ( 2 ) = ( e ) 12 = ( e ) a ⇒ a = 12 y = 4 x 3 − 4 x 2 − 4 ( a − 7 ) x − a y = 4 x 3 − 4 x 2 − 20 x − 12 roots x = − 1 , − 1 , 3 option ( 1 ) ​

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