Question 1114790

Explanation:
the average rate of change of {{{f(x)}}} over an interval [{{{a}}},{{{b}}}] is the {{{slope }}}of the secant line connecting the 2 points: point ({{{a}}},{{{f(a)}}}) and point ({{{b}}},{{{f(b)}}})


 average rate of change ={{{(f(b)-f(a))/(b-a)}}}


given:  {{{f(x)= -2x^2 + 5x - 2}}} on [{{{-1}}},{{{ 1}}}]


-> so, [{{{a}}},{{{b}}}] = [{{{-1}}},{{{ 1}}}] => {{{a=-1}}} and {{{b=1}}}


substitute in: average rate of change ={{{(f(b)-f(a))/(b-a)}}}

 average rate of change ={{{(f(1)-f(-1))/(1-(-1))}}}

find  {{{f(1)}}}:

{{{ f(1)= -2*1^2 + 5*1 - 2=-2+5-2=5-4=1}}}

find  {{{f(-1)}}}:

{{{ f(-1)= -2*(-1)^2 + 5*(-1 )- 2=-2-5-2=-9}}}

plug it in

average rate of change ={{{(1-(-9))/(1-(-1))}}}


average rate of change ={{{(1+9)/(1+1)}}}

average rate of change = {{{10/2}}}

average rate of change ={{{5}}}