Question

What are the points of inflection of k(x)=sinx-(1/4)sin2x

a) -π/3
b) -π/6
c) -π/3, π/3
d) -π/3, 0 , π/3

Answer 1

Option d is correct.

Explanation:

The point of inflection of a function y = f(x) at a pointy c is given by f''(c) = 0.

Now, the given function is

`k(x) = \sin x - (1)/(4)\sin 2x`

Differentiating with respect to x on both sides we get,

`k'(x) = \cos x - (1)/(2) \cos 2x`

Again, differentiating with respect to x on both sides we get,

`k''(x) = - \sin x + \sin 2x = - \sin x + 2 \sin x \cos x`

So, the condition for point of inflection at point c is

k''(c) = 0 = - sin c + 2 sin c cos c

⇒ sin c(2cos c - 1) = 0

⇒ sin c = 0 or
`\cos c = (1)/(2)`

⇒ c = 0 or
`c = \pm (\pi)/(3)`

Therefore, option d is correct. (Answer)