KCET2014MathematicsStraight Lines
The tangent to the curve ( y=x³+1 ) at ( (1,2) ) makes an angle ( ) with y axis, then the value of ( ) is
Options
- A( 03 )
- B( 1 3 )
- C( - 1 3 )
- D(-3 )
Correct answer
C. ( - 1 3 )
Step-by-step solution
Given equation of curve Here [ =90^ + . Then , = (90^ + )=- ] Now, [ = d y d x = d d x (x³+1 )=3 x² ] At point ( (1,2) ), we have ( . d y d x |_ (1,2) = .3 x² |_ (1,2) =3 ) Therefore, required value of ( ) is [ - =- 1 3 ] In the above diagram, ( ) is to be considered as the angle made by tangent with y-axis and not ( ^ ) [for e.g., when we say