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

$\frac{f\mleft(b\mright)-f(a)}{b-a}$

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

$\frac{0-9}{3-0}=-\frac{9}{3}=-3$

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

$-\frac{16-8}{5-(-1)}=\frac{8}{6}=\frac{4}{3}$

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

$\frac{5-5}{2-(-2)}=\frac{0}{4}=0$

the rate of change is zero