Answer:
see explanation
Step-by-step explanation:
given
f'(x) = 12cos x - 4sin x, then
f'([tex]\frac{4\pi }{3}[/tex]) = 12cos([tex]\frac{4\pi }{3}[/tex]) - 4sin([tex]\frac{4\pi }{3}[/tex])
[ cos([tex]\frac{4\pi }{3}[/tex]) = -cos([tex]\frac{\pi }{3}[/tex]), sin([tex]\frac{4\pi }{3}[/tex] = - sin([tex]\frac{\pi }{3}[/tex]) ]
= -12cos([tex]\frac{\pi }{3}[/tex]) + 4sin([tex]\frac{\pi }{3}[/tex])
= - 12 × [tex]\frac{1}{2}[/tex] + 4 × [tex]\frac{\sqrt{3} }{2}[/tex]
= - 6 + 2[tex]\sqrt{3}[/tex] ≈ - 2.536 ( 3 dec. places )
