Question

Given f(x)=x^2-5x find f(a+h)-f(a)/h

Answer 1

this looks suspiciously like the difference quotient

anyway

evaluate each then put them together

`f(a+h)=(a+h)^2-5(a+h)`

`f(a+h)=a^2+2ah+h^2-5a-5h`

`f(a+h)=a^2+2ah-5a-5h+h^2`

`f(a)=a^2-5a`

so
`(f(a+h)-f(a))/(h)=`

`(a^2+2ah-5a-5h+h^2-(a^2-5a))/(h)=`

`(a^2+2ah-5a-5h+h^2-a^2+5a)/(h)=`

`(2ah-5h+h^2)/(h)=`

`2a-5+h`

Answer 2

Answer: 2a -5 + h

Explanation:

f(x) = x² - 5x

f(a + h) = (a + h)² - 5(a + h)

= a² + 2ah + h² - 5a - 5h

f(a) = a² - 5a

f(a + h) - f(a) = a² + 2ah + h² - 5a - 5h - (a² - 5a)

= a² + 2ah + h² - 5a - 5h - a² + 5a

= 2ah - 5h + h²

`(f(a + h) - f(a))/(h) = (2ah - 5h + h^(2))/(h)` = 2a - 5 + h