If we want to compute [tex] f(2+h) [/tex], we have to substitute every occurrence of [tex] x [/tex] with [tex] 2+h [/tex] in the definition of the function:
[tex] f(x)=x^2-11x \implies f(2+h) = (2+h)^2-11(2+h) = 4+4h+h^2-22-11h = h^2-7h-18 [/tex]
Similarly, computing [tex] f(2) [/tex] means to substitute the input with 2:
[tex] f(x)=x^2-11x \implies f(2) = 2^2-11\cdot 2 = 4-22 = -18 [/tex]
So, we have
[tex] f(2+h) - f(2) = h^2-7h-18 - (-18) = h^2-7h [/tex]
And finally
[tex] \dfrac{f(2+h)-f(2)}{h} = \dfrac{h^2-7h}{h} = h-7 [/tex]
