JEE Main2014MathematicsApplication of DerivativesActual

For the curve y =3 , x = e ^ , 0 , the tangent is parallel to x -axis when is:

Options

A3 4
B2
C4
D6

Correct answer

C. 4

Step-by-step solution

Given, y=3 aligned & d y d =3[ (- )+ ( )] & d y d =3 [ ^2 - ^2 ]=3 2 . & and x= e ^ & d x d =e^ + e^ & d x d =e^ ( + ) aligned Dividing (1) by (2) gathered d y d x = 3 2 e^ ( + ) = 3 ( ^2 - ^2 ) e^ ( + ) d y d x = 3( + )( - ) e^ ( + ) d y d x = 3( - ) e^ gathered Given tangent is parallel to x -axis then d y d x =00= 3( - ) e^ or - =0 = =1 = 4 = 4

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