NYU Polytechnic School Of Engineering MA 1154 WORKSHEET # 2

NYU Polytechnic School Of Engineering MA 1154 WORKSHEET # 2

NYU Polytechnic School Of Engineering
MA 1154
WORKSHEET # 2
Date:
Print Name:
Signature:
Section:
Instructor: Dr. Manocha
ID #:
Directions: Complete all questions clearly and neatly. You must show all work to have credit.
Unclear work will not be graded. THIS IS A CRUCIAL HOMEWORK UNDERSTAND IT
WELL FOR YOUR NEXT EXAM.
Problem Possible
1
15
2
15
3
20
4
12
5
12
6
12
7
14
Total
100
Points
Your signature:
(1) Consider the function f (x) = x3 (2x − 7)2 (x + 5).
(a) Find the critical numbers of f (x).
(b) Classify each critical number corresponding to a relative maximum, a relative
minimum, or neither.
(c) Sketch the graph of f .
Your signature:
(2) Consider the given function g(x) = 3x5 − 25x4 + 11x − 17
(a) Determine where the graph of the given function is concave upward and concave
downward.
(b) Find the coordinates of all inflection points.
Your signature:
(3) Consider the function f (x) = x3 − 3x2 + 3x + 1
(a) Determine where the function f is increasing and decreasing.
(b) Find where the graph of f is concave up and concave down.
(c) Find the relative extreme and inflection points
(d) Sketch the graph of f .
Your signature:
(4) Find the absolute maximum and absolute minimum of f (x) = (x2 − 4)5 , −3 ≤ x ≤ 2.
Your signature:
(5) A rectangle is inscribed in a right triangle, as shown in the accompanying figure. If
the triangle has sides of length 5, 12, and 13, what are the dimensions of the inscribed
rectangle of greatest area?
Your signature:
(6) A triangle is positioned with its hypotenuse on a diameter of a circle, as shown in the
accompanying figure. If the circle has radius 4, what are the dimensions of the triangle
of greatest area?
Your signature:
(7) In designing airplanes, an important feature is the so-called drag factor; that is, the
retarding force exerted on the plane by the air. One model measures drag by a function
of the form
B
v2
where v is the velocity of the plane and A and B are constants. Find the velocity
(in terms of A and B) that minimizes F (v). Show that you have found the minimum
rather than a maximum.
F (v) = Av 2 +