Use the difference quotient to calculate the average rate of change across the following intervals. Difference quotient of d(t): 3t2 + 5th – 2 The interval 2 to 3: The interval 2 to 2.5: The interval 2 to 2.1:

Mark Elliott 2022-08-12 Answered
Use the difference quotient to calculate the average rate of change across the following intervals.
Difference quotient of d ( t ) : 3 t 2 + 5 t h 2
The interval 2 to 3:
The interval 2 to 2.5:
The interval 2 to 2.1:
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Answers (1)

Leroy Cunningham
Answered 2022-08-13 Author has 14 answers
(i) The difference quotient for the interval 2 to 3 is 20.
(ii) The difference quotient for the interval 2 to 2.5 is 18.5.
(iii) The difference quotient for the interval 2 to 2.1 is 17.3.
Given a Function d(t) that is Continuous at Interval [a,b], the Difference Quotient associated to the Interval is:
q a b = d ( b ) d ( a ) b a ( 1 )
Where:
d(a)- Function evaluated at lower bound.
d(b)- Function evaluated at upper bound.
In this question, the function is represented by d ( t ) = 3 t 2 + 5 t 2
(i) If we know that and , then the difference quotient is:
q a b = 3 ( 3 ) 2 + 5 ( 3 ) 2 [ 3 ( 2 ) 2 + 5 ( 2 ) 2 ] 3 2 q a b = 20
The difference quotient for the interval 2 to 3 is 20.
(ii) If we know that a=2 and b=2.5, then the difference quotient is:
q a b = 3 ( 2.5 ) 2 + 5 ( 2.5 ) 2 [ 3 ( 2 ) 2 + 5 ( 2 ) 2 ] 2.5 2 q a b = 18.5
The difference quotient for the interval 2 to 2.5 is 18.5.
(iii) If we know that a=2 and b=2.1, then the difference quotient is:
q a b = 3 ( 2.1 ) 2 + 5 ( 2.1 ) 2 [ 3 ( 2 ) 2 + 5 ( 2 ) 2 ] 2.1 2 q a b = 17.3
The difference quotient for the interval 2 to 2.1 is 17.3.

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