MATH 31A: DIFFERENTIAL AND INTEGRAL CALCULUS
FALL 2016 LECTURE 5
GENERAL GUIDELINES
IN SHORT
You need to know everything that was covered in lectures 1-8, and everything
from the textbook that corresponds to what was covered in those lectures. The officia

MATH 31A (Butler)
Practice for Final (A)
Try to answer the following questions without the use of book, notes or calculator;
but you can use the equation sheet posted on the course website. Time yourself and
try to finish the questions in less than three

MATH 31A (Butler)
Practice for Final (C)
Try to answer the following questions without the use of book, notes or calculator;
but you can use the equation sheet posted on the course website. Time yourself and
try to finish the questions in less than three

MATH 31A (Butler)
Practice for Final (B)
Try to answer the following questions without the use of book, notes or calculator;
but you can use the equation sheet posted on the course website. Time yourself and
try to finish the questions in less than three

1. Let
f(a:)m;1;m4 - $3 - gm? + 1.
(a) Find the critical numbers of f.
(0) Find the intervais of increase and decrease of f.
_/
(LAW 61
bi/ 7c Xx? XH
(Vega!) - "
(vi, 0] ~ ' +
(big) ~+ ~ +
[300/ + f "f 2. Calculate the limit, if it exists.
limtanzix
j

MATH 31A (Butler)
Practice for Final (A)
Try to answer the following questions without the use of book, notes or calculator;
but you can use the equation sheet posted on the course website. Time yourself and
try to finish the questions in less than three

Final practice, Math 31A - Lec 1, Fall 2013
Name and student ID:
Question
Points
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
Total:
90
Score
1. (a) (4 points) Find all points x at which the function f (x) = |x2
4x + 3| + x1/3 is not dierentiable.
First |

MATH 31A (Butler)
Practice for Final (C)
Try to answer the following questions without the use of book, notes or calculator;
but you can use the equation sheet posted on the course website. Time yourself and
try to finish the questions in less than three