In the review, the first decision is to read what is being asked. Then, the look of the exercise points to the rule.

1What does the exercise ask for?

a limit (lim appears)

2Replace x with the point. What did you get?

0/0

⟦1⟧factor or rationalize

number ÷ 0, x → ∞ or “asymptotes”

⟦2⟧look at both sides

a derivative

3Does it ask for f″?

yes

⟦4⟧differentiate twice, each time with→⟦3⟧

no, only f′

⟦3⟧outer rule first

maximum, minimum, increase/decrease or sketch

4Is there a quantity to make as large or as small as possible?

yes

⟦5⟧objective, domain, critical points, classification

no, the behavior of the function

⟦6⟧zeros, f′ and f″

an integral

5How do you find the antiderivative?

⟦11⟧ask in this order

basic (it is in the table)

⟦7⟧

composition with the inner derivative

⟦9⟧

product with a factor that simplifies when differentiated

⟦10⟧

6Does it have limits of integration?

yes

⟦8⟧F(b) − F(a), without C

no

⟦7⟧add + C

+Before handing it in

⟦12⟧differentiate the antiderivative; check signs, C and limits

⟦i⟧

Limites e Noções Geométricas