Question

If y=3x^2 - 2x +5

Answer 1

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

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

Part i) x= -3 and x= -1

In this problem we have

$a=--3$

$b=-1$

$f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38$  

$f(b)=f(-1)=3(-1)^{2} -2(-1)+5=10$

Substitute

$\frac{10-38}{-1+3}$

$\frac{-28}{2}$

$-14$

Part ii) x= -3 and x= 0

In this problem we have

$a=--3$

$b=0$

$f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38$  

$f(b)=f(0)=3(0)^{2} -2(0)+5=5$

Substitute

$\frac{5-38}{0+3}$

$\frac{-33}{3}$

$-11$

Part iii) x= (1-h) and x=(1+h)

In this problem we have

$a=-(1-h)$

$b=(1+h)$

$f(a)=f(1-h)=3(1-h)^{2} -2(1-h)+5=3(1-2h+h^2)-2+2h+5=3-6h+3h^2+2h+3=3h^2-4h+6$  

$f(b)=f(1+h)=3(1+h)^{2} -2(1+h)+5=3(1+2h+h^2)-2-2h+5=3+6h+3h^2-2h+3=3h^2+4h+6$  

Substitute

$\frac{(3h^2+4h+6)-(3h^2-4h+6)}{1+h-(1-h)}$

$\frac{8h}{2h}$

$4$