calculus question

Question

If f (t)=t2 + 4t + 3, find [ f(t + h) -f (t)]/h.

Answer 1

f(t) = t² + 4t + 3

 

[f(t+h) - f(t)] / h = [(t+h)² + 4(t+h) + 3 - (t² + 4t + 3)] / h

 

                          = [t² + 2th + h² + 4t + 4h + 3 - t² - 4t - 3] / h

 

                          = [2th + h² + 4h] / h

 

                          = h(2t + h + 4) / h  = 2t + h + 4