Question

If x = 3 tan t and y = 3 sec t, then the value of d²y/dx² at t = π/4, is :
(A) 3/(2√2)
(B) 1/(3√2)
(C) 1/6
(D) 1/(6√2)

Answer 1

Answer:

the answer for this is B

Answer 2

The value of d^2y/dx^2 at t=π/4 is 1/6√2

1.Given y=3 sect

the derivative of sect is sect tant

dy/dt=3sect.tant

2.x=3tant

the deivative of tant is sec^2t

dx/dt =3 sec^2t

3.dy/dx=dy/dt.dt/dx=sint(cancelling dt in numerator and denominator gives dy/dx which is what we want)

4.d^2y/dx^2= d/dx (dy/dx)( for .d^2y/dx^2 we need to find derivative of dy/dx again )

=1/3 cos^3t

= 1/3 cos(π/4)^3( substituting value of t=π/4 ) we get

=1/6√2