Consider the function #f(x) = (x)/(x+2)# on the interval [1, 4], how do you find the average or mean slope of the function on this interval?

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Answer 1 · 2017-09-04T14:34:08

The mean slope is #=1/9#

The average or mean slope of the function #y=f(x)# on an interval #[x_1,x_2]# is

#(Deltay)/(Deltax)=(f(x_2)-f(x_1))/(x_2-x_1)#

Here,

#y=f(x)=x/(x+2)#

And the interval is #=[1,4]#

Therefore,

#f(1)=1/(1+2)=1/3#

#f(4)=4/(4+2)=4/6=2/3#

So,

#(Deltay)/(Deltax)=(f(4)-f(1))/(4-1)=(2/3-1/3)/(4-1)=1/3*1/3=1/9#