MAC 2311 EXAM 2 Review - M. Rahmanpage 1

MAC 2311 EXAM 2 Review - M. RAHMANPage 1

MAC 2311/SP10/EXAM 2/REVIEW

** To answer all questions in EXAM2, you must need to be the master of everything that I covered in sections 3.5, 3.6, 3.7, 4.1-4.6.

*** Do all homework problems listed in the assignments, read class notes, and quizzes.

Goal:

Know implicit differentiation

Know the derivatives of inverse trigonometric functions.
Know how to set up and solve related rate problem
Know how to find critical numbers
Know how to find intervals on which the function is increasing and decreasing
Know how to find extrema (max/min) using first derivative test
Know how to find intervals on which the function is concave upward and concave downward.
Know Rolle’s theorem and Mean Value theorem and its application
Know how to find point of inflection
Know how to find extrema (max/min) using second derivative test
Analyze and sketch the graph

Sample problem1: Find the derivatives of each of the following functions.

i. ii.

iii. iv.

Sample problem2. A circle of pollution is spreading from a broken underwater waste disposal pipe, with the radius increasing at the rate of 4ft/minute. Find the rate of change of the area of the circle when the radius is 7 ft.

Sample problem3. A baseball diamond has the shape of a square with sides 90 feet long (see figure). A player running from second base to a third base at a speed of 28 feet per second is 30 feet from third base. At what rate is the player’s distance s from home plate changing?

Sample problem 4.Let

a) Find critical numbers.

b) Find intervals on which the function is increasing and decreasing.

c) Find intervals on which the function is concave upward and concave downward.

d) Find point of inflection.

e) Find all relative extrema.

f) Sketch the graph of f(t).

Sample problem5. Consider the function . Determine whether the Mean Value Theorem can be applied to f on the closed interval If the Mean Value Theorem can be applied , find all values of c in the open interval such that

Sample problem6. Find the relative extrema:

Sample problem7. Find the limit.

a) b) c) d)

Sample problem8 (hard). Consider the function (goal: analyze and sketch the graph).

a) Find intercepts;

b) Find asymptotes;

c) Find critical numbers;

d) Find possible point of inflection;

e) Find domain;

f) Find axis of symmetry;

g) Find intervals on which the function is increasing or decreasing;

h) Find relative extrema;

i) Find intervals on which function is concave up or down; and

k) Sketch the graph

(Hint: Try to a easy one first from section 4.6)