Question

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

Minimum Value =

Maximum Value=

Answer 1

Given g(θ) = 5θ - 6sin(θ)

differentiate with respect to θ, we get

dg/dθ =5 - 6cos(θ)

for critical points dg/dθ=0

                 ==>5-6cosθ=0

                ==>cosθ=5/6

                ==>θ=cos-1(5/6)

Also g(0) = 5*0 - 6sin(0) =0

g(pi/2) = 5*(pi/2) - 6sin(pi/2) =5*(pi/2) - 6 = 1.854

g(cos-1(5/6)) = 5*(cos-1(5/6)) - 6*sin(cos-1(5/6)) =-0.388

maximum value = 1.854

minimum value = -0.388