# Calculus I Exam Review

The first exam will cover chapter 4 of Stewart’s text,
Single Variable Calculus, 6e except

for sections 4.6 and 4.8. Exam date is Tuesday, October 28 — start time is
7:45am, finish

time is 9:15am plus a 5-minute grace period. The exam will include several
computational

problems and one proof. There will definitely be a question from section 4.5
asking you

to “put it all together” and a question from section 4.7. I may also explicitly
ask for a

definition or theorem statement, though True-False type questions might also
occur. The

chapter review provides a good source of problems for practice and
consideration. As you

prepare for the exam, please remember the writing expectations that I have set
forth.

Class-time on October 27th is devoted to your questions.

**Definitions and facts to know**

• absolute maximum, maximum value, absolute minimum,
minimum value

• local maximum, local minimum

• limit at infinity and for r > 0 a rational
number.

**Theorems to know**

• Extreme Value Theorem

• Fermat’s Theorem

• Rolle’s Theorem

• Mean Value Theorem

• Closed Interval method

**Computational problems**

• Find critical points. Use the first derivative test
and/or second derivative test determine

nature of a critical point.

• Compute limits at infinity to determine horizontal asymptotes.

• Sketch a function by method introduced in Section 4.5: find domain,
x-intercepts,

y-intercept, symmetry, horizontal and vertical asymptotes, intervals of increase
and

decrease, local maximum and minimum, concavity and points of inflection.

• Find the antiderivative of a polynomial and sin x and cos x

**Proofs**

• Prove Fermat’s theorem

• Prove Rolle’s Theorem

• Prove the Mean Value Theorem