Question

The function y = 1 + sin x is maximum, when x = ______ 

Options

• `(3pi)/2`

• `pi/2`

• π

• `-pi/6`

Answer 1

The function y = 1 + sin x is maximum, when x = `underline(pi/2)`.

Explanation:

y = 1 + sinx

∴ y' = cosx

For maximum or minimum,

y' = 0 ⇒ cosx = 0 ⇒ `x = pi/2, (3pi)/2`

Now, y'' = -sinx

⇒ `y^{''}(pi/2) = -1 < 0` and `y^{''}((3pi)/2) = 1 > 0`

∴ y is maximum w en x = `pi/2`.