Question

Find the maximum and minimum values of the function g ( θ ) = 5 θ − 6 sin ( θ ) on the interval [ 0 , π /2 ]

Answer 1

Answer:

Minimum value of the given function is  0

Maximum value of the given function

                                         $\frac{5\pi -12}{6}$

Step-by-step explanation:

Step(i):-

Given function    g ( θ ) = 5 θ − 6 sin ( θ )  ...(i)

Differentiating equation (i) with respective to 'θ'

                            g¹ ( θ ) = 5  − 6 cos ( θ ) ...(ii)

                          g¹ ( θ ) = 5  − 6 cos ( θ ) =0

                          5 = 6 cos ( θ )

                       cos ( θ ) = 5 /6  

                               

Step(ii):-                        

Again Differentiating equation (ii) with respective to 'θ'

                              g¹¹ ( θ ) =   − 6 (-sinθ )  = 6sinθ

Given interval

                         θ = 0 and   θ= π/2

                     g ( 0 ) = 5 (0) − 6 sin ( 0 ) = 0

                     g(π/2) = 5(π/2) - 6 sin (π/2)

                               =  5(π/2) - 6

                               = $\frac{5\pi -12}{6}$