Consider the function # f(x)=1/sqrt(x+2)# on the interval [-1, 23], how do you find the average or mean slope of the function on this interval?

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Answer 1 · 2017-05-12T15:12:37

The mean slope is #=-1/30#

The mean slope of a function #f(x)# over an interval #[a,b]# is

#=(f(b)-f(a))/(b-a)#

Here,

#f(x)=1/sqrt(x+2)#

#f(-1)=1/sqrt(-1+2)=1#

#f(23)=1/sqrt(23+2)=1/5#

Therefore,

the mean slope is

#=(f(23)-f(-1))/(23-(-1))#

#=(1/5-1)/(24)#

#=-4/5*1/24=-1/30#