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Rama09 [41]
4 years ago
6

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

Mathematics
1 answer:
notsponge [240]4 years ago
7 0

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

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