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Algebraic Methods - Calculus - Exam, Exams of Calculus

Birla Institute of Technology and ScienceCalculus

This is the Exam of Calculus which includes Constant, Constant Height, Concave Up, Antiderivative, Compare, Natural Domain, Average, Range, Natural Domain etc. Key important points are: Algebraic Methods, Directions, Domain, Proper Justiffication, Domain, Algebraic Methods, Determine, Function, Second Derivative, Infection Point

Typology: Exams

2012/2013

Uploaded on 03/06/2013

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Math 105a Name
Exam 1
10/7/11
Read directions carefully and show all your work. Partial credit will be assigned based upon the correctness,
completeness, and clarity of your answers. Correct answers without proper justification or those that use
unapproved short-cut methods will not receive full credit.
1. (10 pts) What is the domain of f(x) = √x
(x+ 1)(x−2)?
2. (10 pts) Use algebraic methods to determine if the function f(x) = x5−3x3+xis even, odd, or neither?
3. (10 pts) Consider a function fwith second derivative f00(x) = (4x4+ 6x2)ex2.
Is x= 0 an inflection point for f? Justify your answer.
1
pf3
pf4

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Math 105a Name Exam 1 10/7/

Read directions carefully and show all your work. Partial credit will be assigned based upon the correctness, completeness, and clarity of your answers. Correct answers without proper justification or those that use unapproved short-cut methods will not receive full credit.

  1. (10 pts) What is the domain of f (x) =

x (x + 1)(x − 2)

  1. (10 pts) Use algebraic methods to determine if the function f (x) = x^5 − 3 x^3 +x is even, odd, or neither?
  2. (10 pts) Consider a function f with second derivative f ′′(x) = (4x^4 + 6x^2 )ex

2 . Is x = 0 an inflection point for f? Justify your answer.

  1. (12 pts) Consider the graph of f ′, NOT f , provided below.

(a) On what interval(s) is f increasing?

(b) At which labeled point(s) is f greatest?

(c) At which labeled point(s) is f least?

(d) At which labeled point(s) does f have a local maximum?

  1. (13 pts) Use the limit definition of the derivative to find f ′(0) when f (x) =

x + 1

  1. (15 pts) Imagine that you are on the surface of the moon throwing a rock straight up in the air. The rock is released at a height of 1.5 meters with an initial velocity of 25 m/sec. On the moon, the acceleration due to gravity is approximately 1.62 m/sec^2. What is the maximum height the rock will go?
  2. (10 pts) Find the equation of the line tangent to the graph of f (x) = 2

x + 3x at x = 1.