calculate and simplify f(5+deltat)-f(5) all over delta t

Question

the model is f(t) = 7-2t+11t^2 for 3lessthanequal t lessthanequal 11

Answer 1

f(5+∆t) = 7 - 2(5+∆t) + 11(5 + ∆t)^2
f(5) = 7 - 10 + 275 = 272
so ( f(5+∆t) - f(t) )/∆t
= ( 7 - 10 - 2∆t + 11(25 + 10∆t + ∆t)^2 - 272)/∆t
= ( -3 - 2∆t + 275 + 110∆t + 11(∆t)^2 -272)/∆t
=(11(∆t)^2 + 108∆t)/∆t
= 11∆t + 108