Question

Given f(x) = 5x^2 - 2x + 3, find and simplify (f(x+h)-f(x))/h

A. 10x + 5h - 2
B. 5h - 2
C. - 4x + 5h +4
D. 2x + 5h + 6
E. 1

Answer 1

A

Explanation:

we require to simplify

`(f(x+h)-f(x))/(h)`

substitute x = x + h into f(x)

=
`(5(x+h)^2-2(x+h)+3-(5x^2-2x+3))/(h)` ← expand squared factor using FOIL

=
`(5(x^2+2hx+h^2)-2x-2h+3-(5x^2-2x+3))/(h)` ← distribute parenthesis on numerator

=
`(5x^2+10hx+5h^2-2x-2h+3-5x^2+2x-3)/(h)` ← collect like terms on numerator

=
`(10hx+5h^2-2h)/(h)` ← factor out common factor h from each term on numerator

=
`(h(10x+5h-2))/(h)` ← cancel h on numerator/denominator

= 10x + 5h - 2