Question

Does anyone know how to solve the second half of this question?

Answer 1

see explanation

Explanation:

given

f'(x) = 12cos x - 4sin x, then

f'(
`(4\pi )/(3)`) = 12cos(
`(4\pi )/(3)`) - 4sin(
`(4\pi )/(3)`)

[ cos(
`(4\pi )/(3)`) = -cos(
`(\pi )/(3)`), sin(
`(4\pi )/(3)` = - sin(
`(\pi )/(3)`) ]

= -12cos(
`(\pi )/(3)`) + 4sin(
`(\pi )/(3)`)

= - 12 ×
`(1)/(2)` + 4 ×
`(√(3) )/(2)`

= - 6 + 2
`√(3)` ≈ - 2.536 ( 3 dec. places )