Write and simplify the difference quotient for the function b(t)= 3t^2-4t+5 over the interval [7,7+h]

Answer 1

b(t+h)-b(t)
=(3(t+h)^2-4(t+h)+5) - (3t^2-4t+5)
=(3t²+6ht+3h² -4t-4h + 5) - (3t^2-4t+5)
=6ht+3h²
Substitute t=7 to get an expression in terms of h.