How do you find the instantaneous rate of change for f ( x ) = x

deceptie3j

deceptie3j

Answered question

2022-06-25

How do you find the instantaneous rate of change for f ( x ) = x 2 2 x 1 for x=2?

Answer & Explanation

svirajueh

svirajueh

Beginner2022-06-26Added 29 answers

Explanation:
The rate of change is the derivative of the function. To find this we use the quotient rule d d x ( f ( x ) g ( x ) ) = g ( x ) f ( x ) g ( x ) f ( x ) g ( x ) 2
d d x ( f ( x ) g ( x ) ) = ( x 1 ) 2 x 1 ( x 2 2 ) ( x 1 ) 2
d d x ( f ( x ) g ( x ) ) = 2 x 2 2 x x 2 + 2 ( x 1 ) 2 = x 2 2 x 2 ( x 1 ) 2
if x=2 the rate of change 2 2 2 2 2 ( 2 1 ) 2 = 2 1 = 2

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