Question

F(x)=9-x^2Average rate of change x=0 to x=3x=-1 to x=5x=-2 to ×=2

Answer 1

f(x)=9-x^2

Average rate of change

x=0 to x=3

x=-1 to x=5

x=-2 to ×=2​

we know that

The average rate of change is equal to

`(f\mleft(b\mright)-f(a))/(b-a)`

Part 1) we have

a=0

b=3

f(a)=f(0)=9-(0)^2=9

f(b)=f(3)=9-(3^2)=0

substitute the given values in the expression above

`(0-9)/(3-0)=-(9)/(3)=-3`

the rate of change is -3

Part 2) we have

a=-1

b=5

f(a)=f(-1)=9-(-1)^2=8

f(b)=f(5)=9-(5)^2=-16

substitute the given values in the expression above

`-(16-8)/(5-(-1))=(8)/(6)=(4)/(3)`

the rate of change is 4/3

Part 3) we have

a=-2

b=2

f(a)=f(-2)=9-(-2)^2=5

f(b)=f(2)=9-(2)^2=5

substitute

`(5-5)/(2-(-2))=(0)/(4)=0`

the rate of change is zero