KCET 2014 Math Solved Paper

Given equation of curve
y=x3+1Here Now,
tan‌θ=‌

dy

dx

=‌

d

dx

(x3+1)=3x2
At point (1,2), we have

dy

dx

|(1,2)=3x2|(1,2)=3
Therefore, required value of θ is
−cot‌ϕ=−‌

1

3

In the above diagram, θ is to be considered as the angle made by tangent with y-axis and not θ′ [for e.g., when we say angle made by a line with x-axis, it is the angle measured from x-axis to the line in anticlockwise direction, unless mentioned otherwise]Here we consider θ as the angle made by the line with positive x-axis and not θ'