Question

let y=x^2+1 Find the average rate of change of y with respect to x over the interval [3,5]
​

Answer 1

Answer:

Step-by-step explanation:

Calculate  

y

(

4

)

as,

y

(

4

)

=

2

(

4

)

+

2

⇒

y

(

4

)

=

10

Calculate  

y

(

−

3

)

as,

y

(

−

3

)

=

2

(

−

3

)

+

2

⇒

y

(

−

3

)

=

−

4

By using the following relation, the average rate of change of y with respect to x over the given interval is calculated as,

Average

 

rate

=

y

(

4

)

−

y

(

−

3

)

4

−

(

−

3

)

⇒

Average

 

rate

=

10

−

(

−

4

)

4

−

(

−

3

)

⇒

Average

 

rate

=

14

7

⇒

Average

 

rate

=

2

Thus, the average rate of change of y with respect to x over the given interval is 2.