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