Question

Question 6: Difference Quotient​

Answer 1

see explanation

Explanation:

(a)

f(x) = 2x + 5 , then difference quotient is

`(2(x+h)+5-(2x+5))/(h)`

=
`(2x+2h+5-2x-5)/(h)`

=
`(2h)/(h)`

= 2

(b)

f(x) = 3x² + x , then difference quotient is

`(3(x+h)^2+(x+h)-(3x^2+x))/(h)`

=
`(3(x^2+2hx+h^2+x+h-3x^2-x)/(h)`

=
`(3x^2+6hx+3h^2+x+h-3x^2-x)/(h)`

=
`(6hx+3h^2+h)/(h)`

=
`(h(6x+3h+1))/(h)`

= 6x+3h+1