F(x) = 3 sin x + 3 cos x, 0 ≤ x ≤ 2π. Find the interval in which f is concave up and concave down. Find the inflection points

Solution:

The interval in which the function is concave upwards is from 0 to π/3 and concave downwards from π/3 to 2π.

It is evident from the graph below.

The first inflection point is (3π/4, 0) and the second inflection point lies between (5π/3, -1.09) and (11π/6, 1.11)

F(x) = 3 sin x + 3 cos x, 0 ≤ x ≤ 2π. Find the interval in which f is concave up and concave down. Find the inflection points

Summary:

The interval in which f is concave upwards is from 0 to π/3 and concave downwards from π/3 to 2π. The first inflection point is (3π/4, 0) and the second inflection point lies between (5π/3, -1.09) and (11π/6, 1.11).