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

User Tuntable
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1 Answer

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19 votes

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

User Shekinah
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