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FInd the average rate of change

0 votes
FInd the average rate of change of f(x)=3x^2-7 between (a, f(a)) and (a+h, f(a+h)). Simplify your answer completely.
asked Sep 8, 2018 in ALGEBRA 1 by skylar Apprentice

1 Answer

0 votes

The function is f(x) = 3x^2 - 7

Substitute x = a in f(x)

f(a)  =  3a^2 - 7

Substitute x = a + h in f(x)

f(a + h)  =  3(a + h)^2 - 7
 
             =  3(a^2 + h^2 + 2ah) - 7
 
(a + h)  =  3a^2 + 3h^2 + 6ah - 7
 
The rate of change is 
 
[f(a + h) - f(a) ] / (a + h - a )  =  [ (3a^2 + 3h^2 + 6ah - 7 ) -  ( 3a^2 - 7 ) ] / h
 
                                                    =  [ 3a^2 + 3h^2 + 6ah - 7  -   3a^2 + 7  ] / h
 
                                                    =  [ 3h^2 + 6ah ] / h
 
                                                    =  h (3h + 6a) / h
 
[f(a + h) - f(a) ] / (a + h - a )  =  3h + 6a
 
Answer :
 
[f(a + h) - f(a) ] / (a + h - a )  =  3h + 6a
 
answered Sep 9, 2018 by homeworkhelp Mentor

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