Answer:
Part i) -14
Part ii) 11
Part iii) 4
Step-by-step explanation:
we know that
The average rate of change or slope using the difference quotient formula is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Part i) x= -3 and x= -1
In this problem we have
[tex]a=--3[/tex]
[tex]b=-1[/tex]
[tex]f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38[/tex]
[tex]f(b)=f(-1)=3(-1)^{2} -2(-1)+5=10[/tex]
Substitute
[tex]\frac{10-38}{-1+3}[/tex]
[tex]\frac{-28}{2}[/tex]
[tex]-14[/tex]
Part ii) x= -3 and x= 0
In this problem we have
[tex]a=--3[/tex]
[tex]b=0[/tex]
[tex]f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38[/tex]
[tex]f(b)=f(0)=3(0)^{2} -2(0)+5=5[/tex]
Substitute
[tex]\frac{5-38}{0+3}[/tex]
[tex]\frac{-33}{3}[/tex]
[tex]-11[/tex]
Part iii) x= (1-h) and x=(1+h)
In this problem we have
[tex]a=-(1-h)[/tex]
[tex]b=(1+h)[/tex]
[tex]f(a)=f(1-h)=3(1-h)^{2} -2(1-h)+5=3(1-2h+h^2)-2+2h+5=3-6h+3h^2+2h+3=3h^2-4h+6[/tex]
[tex]f(b)=f(1+h)=3(1+h)^{2} -2(1+h)+5=3(1+2h+h^2)-2-2h+5=3+6h+3h^2-2h+3=3h^2+4h+6[/tex]
Substitute
[tex]\frac{(3h^2+4h+6)-(3h^2-4h+6)}{1+h-(1-h)}[/tex]
[tex]\frac{8h}{2h}[/tex]
[tex]4[/tex]
