Math problems

Anonymous
timer Asked: Jun 19th, 2018
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Question description

Sketch the graph of a continuous function f with:

(a) f(1) = 3, f 0 (1) = 0 and the point (1, 3) a relative maximum of f .

(b) f(2) = 1, f 0 (2) = 0 and the point (2, 1) a relative minimum of f .

(c) f(3) = 5, f is not differentiable at x = 3, and the point (3, 5) a relative maximum of f .

MATH 140 Quiz 3 NAME:____________________________ INSTRUCTIONS • • • • • The quiz is worth 100 points. There are five problems (each worth 20 points). This quiz is open book and open notes. This means you may refer to your textbook, notes, and online classroom materials. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our syllabus. You must show all work in order to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor. Please carefully review How to submit quizzes and exams in our Syllabus. If you have any questions, please feel free to email me at: Emailed quizzes and exams will not be accepted (they crash my email system). Thank you for understanding. Best of luck! ☺ MULTIPLE CHOICE Select the best answer choice. Write your answer choices below: (1) _____ (2) _____ (3) _____ (4) _____ (5) _____ 1) ______ Find the intervals on which the function 𝑓(𝑥) = 𝑥 2⁄3 (10 − 𝑥) is increasing and decreasing. Sketch the graph of 𝑦 = 𝑓(𝑥) and identify any local maxima and minima. Any global extrema should also be identified. (A) 𝑓(𝑥) is decreasing on the interval (−∞, 0) ∪ (4, ∞); increasing on (0, 4) (B) 𝑓(𝑥) is increasing on the interval (−∞, 0) ∪ (4, ∞); decreasing on (0, 4) (C) 𝑓(𝑥) is decreasing on the interval (−∞, 10) ∪ (10, ∞) (D) 𝑓(𝑥) is increasing on the interval (−∞, 0) ∪ (0, ∞) (E) none of the above (2) ______ Sand falling from a hopper at 10𝜋 𝑓𝑡 3 ⁄𝑠𝑒𝑐 forms a conical sand pile whose radius is always equal to its height. How fast is the radius increasing when the radius is 5 𝑓𝑡? (A) 5 𝑓𝑡⁄𝑠𝑒𝑐 (B) 10 𝑓𝑡⁄𝑠𝑒𝑐 (C) 2⁄5 𝑓𝑡⁄𝑠𝑒𝑐 (D) not enough information (E) none of the above ℎ 𝑟 (3) _____ Find the values of 𝑎 and 𝑏 for which the function 𝑔 below is differentiable (𝐴) 𝑎 = 1, 𝑏 = −1 (𝐵) 𝑎 = 1, 1 (𝐶) 𝑎 = , 2 𝑏=− 1 (𝐷) 𝑎 = − , 2 1 2 1 𝑏=− 2 𝑏=1 (𝐸) None of the above 𝑎𝑥 + 𝑏 𝑔(𝑥) = { 3 𝑎𝑥 + 𝑥 + 2𝑏 𝑥 ≤ −1 𝑥 > −1 (4) ______ Find 𝑓 ′ (𝑥) given 1 𝑓(𝑥) = 1+ 1 1+ (𝐴) 1 (𝑥 + 2)2 (𝐵) − 1 (2𝑥 + 1)2 (𝐶) − (1 + (1 + 𝑥 −1 )−1 )−2 ∙ (−(1 + 𝑥 −1 )) (𝐷) −(1 + (1 + 𝑥 −1 )−1 )−2 ∙ −𝑥 −2 (𝐸) None of the above −2 1 𝑥 (5) _____ Find the derivative of 𝑓 at 𝑥 = 0 provided it exists. If it does not exist, explain. 𝑓(𝑥) = { (𝐴) 𝑓 ′ (0) = 0 (𝐵) 𝑓 ′ (0) = 1 2 1 − cos 𝑥 𝑥 0 (𝐶) 𝑓 ′ (0) = 1 𝑥≠0 𝑥=0 (𝐷) 𝑓 ′ (0) 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑒𝑥𝑖𝑠𝑡 (𝐸) 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒

Tutor Answer

Authenticw
School: UCLA

Hey there! Review the attached file and let me know if you need anything.

MATH 140 Quiz 3

NAME: ____________________________

INSTRUCTIONS







The quiz is worth 100 points. There are five problems (each worth 20 points).
This quiz is open book and open notes. This means you may refer to your textbook,
notes, and online classroom materials. You may take as much time as you wish, provided
you turn in your quiz no later than the due date posted in our syllabus.
You must show all work in order to receive full credit. If you do not show your
work, you may earn only partial or no credit at the discretion of the professor.
Please carefully review How to submit quizzes and exams in our Syllabus. If you have
any questions, please feel free to email me at:
Emailed quizzes and exams will not be accepted (they crash my email system). Thank
you for understanding. Best of luck! ☺

MULTIPLE CHOICE Select the best answer choice. Write your answer choices
below:
(1)

__A___

(2)

_ C____

(3)

__E___

(4)

__B___

(5)

___A__

1) __A__...

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Anonymous
Excellent job

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