Let fxx2x Evaluate fafa h and the difference quotient fahfa

Let f(x)=x^2-x. Evaluate f(a),f(a + h) and the difference quotient f(a+h)-f(a)/h.Simplify each answer. Show all your work.

Solution

f(x) = x^2 -x

Plug x= a ; f(a ) = a^2 - a

plug x= a+h ; f(a+h) = (a+h)^2 - (a+h)

[ f(a+h) - f(a) ]/h = [ (a+h)^2 - (a+h) - (a^2 -a)]/h

=[a^2 +h^2 +2ah -a -h -a^2 +a]/h

= [h^2 +2ah -h]/h

=h +2a -1