Given f(a)=1/(x+11) find the average rate of change of f(x) on the interval [4, 4 + h)

sincsenekdq

sincsenekdq

Answered question

2022-09-11

Given f ( x ) = 1 x + 11 , find the average rate of change of f(x) on the interval [4,4+h].

Answer & Explanation

lloviznennj

lloviznennj

Beginner2022-09-12Added 12 answers

Given that,
f ( x ) = 1 x + 11
Now, f ( x ) + h = 1 ( x + h ) + 11 = 1 ( 11 + x ) + h f ( 4 + h ) = 1 ( 11 + 4 ) + h = 1 15 + h f ( 4 ) = 1 4 + 11 = 1 15
Hence, average rate of change of f(x) on the interval [4,4th] is
f ( 4 + h ) f ( 4 ) h = 1 15 + h 1 15 h = 1 h [ 1 15 + h 1 15 ] = 1 h [ 15 ( 15 + h ) ( 15 + h ) 15 ] = h h [ ( 15 + h ) 15 ] = 1 15 ( 15 + h )

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