Question

If f(t) = 2t – t2, what is (f(t + h) – f(t)) / h?

Answer 1

[f(t+h)-f(t)] / h   = 2 - 2t -h

Step-by-step explanation:

Given: f(t) = 2t – t²

Find: [f(t+h)-f(t)] / h

Solution:

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

= (2t + 2h -t² –2th - h² – 2t +t²) / h

= [ (2t - 2t) + (2h) + (-t² +t²) + (-2th) + (-h²) ] / h

= (2h -2th -h²) / h

= [h * (2 -2t -h) ] / h

= 2 - 2t -h