Question

I dont understand how to answer this. I tried to find the second derivative. ​

Answer 1

Answer:

(B) π/12 + π/6 k

Step-by-step explanation:

Points of inflection are where f"(x) = 0 and changes signs.

f(x) = cos²(3x)

f(x) = (cos(3x))²

f'(x) = 2 (cos(3x))¹ × -sin(3x) × 3

f'(x) = -6 sin(3x) cos(3x)

Using double angle formula:

f'(x) = -3 sin(6x)

f"(x) = -3 cos(6x) × 6

f"(x) = -18 cos(6x)

0 = -18 cos(6x)

0 = cos(6x)

6x = π/2 + 2πk or 6x = 3π/2 + 2πk

We can simplify this to:

6x = π/2 + πk

x = π/12 + π/6 k