Question 1179648
the avarage rate of change in given interval is:

given:

{{{y=4sin(x)-7}}}
recall: {{{y=f(x)}}}
{{{pi<=x<=4pi/3}}}

=>


the avarage rate ={{{(f(x[2])-f(x[1]))/(x[2]-x[1])}}}


if {{{x[1]=pi}}} find


{{{f(x[1])=4sin(pi)-7}}}....{{{sin(pi)=0}}}

{{{f(x[1])=4*0-7}}}

{{{f(x[1])=-3}}}



if {{{x[2]=4pi/3}}} find

{{{f(x[2])=4sin(4pi/3)-7}}}....{{{sin(4pi/3)=-sqrt(3)/2}}}

{{{f(x[2])=4*(-sqrt(3)/2)-7}}}

{{{f(x[2])=-7 - 2sqrt(3)}}}


then


the avarage rate ={{{(-7 - 2sqrt(3)-(-3))/(4pi/3-pi)}}}

the avarage rate ={{{(-7 - 2sqrt(3)+3)/(pi/3)}}}

the avarage rate ={{{-(6 (2 + sqrt(3)))/pi}}}-> exact solution

or

the avarage rate ={{{-7.13}}}