(21)
Suppose, we have to find average rate of change of f(x) on [a,b]
we can use average rate of change formula
[tex] A=\frac{f(b)-f(a)}{b-a} [/tex]
we are given
[tex] f(x)=x^2+4x+1 [/tex]
[tex] f(4)=4^2+4*4+1 [/tex]
[tex] f(4)=33 [/tex]
[tex] f(-1)=(-1)^2+4*(-1)+1 [/tex]
[tex] f(-1)=-2 [/tex]
[tex] A=\frac{f(4)-f(-1)}{4+1} [/tex]
[tex] A=\frac{33-(-2)}{4+1} [/tex]
[tex] A=7 [/tex].............Answer
(22)
Suppose, we have to find average rate of change of f(x) on [a,b]
we can use average rate of change formula
[tex] A=\frac{f(b)-f(a)}{b-a} [/tex]
on [-2,3]
[tex] A=\frac{g(3)-g(-2)}{3+2} [/tex]
we can look at the table
g(3)=12.5
g(-2)=400
so, we can plug these values
[tex] A=\frac{12.5-400}{3+2} [/tex]
[tex] A=-77.5 [/tex].........Answer
