Question

[f(x)= 3sin x + 5cos x, on }(-π, π)] a) Determine the intervals on which f is concave un and concava down. f is concave up on:

Answer 1

To determine the intervals on which f is concave up and concave down, find the second derivative of f(x). Set the second derivative greater than zero to find the intervals where f is concave up. Set it less than zero to find the intervals where f is concave down.

Step-by-step explanation:

To determine the intervals on which f is concave up and concave down, we need to find the second derivative of f(x). The second derivative of f(x) is given by: f''(x) = -3sin(x) - 5cos(x).

To find the intervals where f is concave up, we need to find where f''(x) > 0. Set f''(x) > 0 and solve for x:

-3sin(x) - 5cos(x) > 0

Solving this inequality will give us the intervals where f is concave up. Similarly, to find the intervals where f is concave down, we need to find where f''(x) < 0.