Question

Use Newton's method to find the absolute maximum value of the function
f(x) = 3x sin x,

0 ≤ x ≤ π
correct to six decimal places.

Answer 1

Geez... this makes my head want to asplode.

Answer 2

Set the derivative equal to 0 to find the critical points, then find the intervals where it switches from positive to negative or vice versa. Negative to positive indicates a a local minimum, while positive to negative indicates a local maximum!