Find the average rate of change of the absolute value

Mary Jackson

Mary Jackson

Answered question

2021-12-10

Find the average rate of change of the absolute value function
(a)on [h,0] if h<0.
(b) on [0,h] if h>0.
(c) Express parts (a) and (b) as a piecewise function of h.

Answer & Explanation

scomparve5j

scomparve5j

Beginner2021-12-11Added 38 answers

Step 1
we know absolute value function is
f(x)=|x|
a.
average rate of change on[h,0] if h<0
let A represent average rate of change then
A=f(h)f(0)h0
A=|h||0|h0
since h<0 therefore |h|=-h
A=hh
A=-1
Step 2
b.
average rate of change on[0,h] ,if h>0
A=f(h)f(0)h0
A=|h||0|h0
since h>0 therefore |h|=h
A=hh
A=1
c.
piecewise function
A={1,h<01,h>0

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