Question

If `y=sin(ax+b)`, then what is `(d^(2)y)/(dx^(2))` at `x=-(b)/(a)`, where a, be are constants and `a ne 0`?

Answer 1

Correct Answer - A
Let y = sin(ax + b)
`rArr (dy)/(dx) = a cos(ax + b)`
`rArr (d^(2)y)/(dx^(2))= -a^(2) sin(ax+b)`
Now, `(d^(2)y)/(dx^(2)) "at x" = -(b)/(a)` is
`-a^(2)sin(a(-(b)/(a))+b)=-a^(2) sin 0 = 0`