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

Answer:

Option d is correct.

Step-by-step 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

$k(x) = \sin x - \frac{1}{4}\sin 2x$

Differentiating with respect to x on both sides we get,

$k'(x) = \cos x - \frac{1}{2} \cos 2x$

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 $\cos c = \frac{1}{2}$

⇒ c = 0 or $c = \pm \frac{\pi}{3}$

Therefore, option d is correct. (Answer)