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Math 122 Exam 2 Study Guide

by: fippsln Notetaker

Math 122 Exam 2 Study Guide Math 122

fippsln Notetaker

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This study guide covers practice problems and examples covered in chapter 3. If there are any problems with the study guide please let me know! You can email me at You may al...
Larita B. Hipp
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This 9 page Study Guide was uploaded by fippsln Notetaker on Sunday October 16, 2016. The Study Guide belongs to Math 122 at University of South Carolina - Columbia taught by Larita B. Hipp in Fall 2016. Since its upload, it has received 16 views.


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Date Created: 10/16/16
Math 122 (Hipp)  Exam 2 Study Guide (section 3.1­3.4) 1)  Find the derivative. a. f(x)=6 b. f(x)=7x+3 9 c. f(x)=x −4 d. f(x)=  x 1 e. f(x)= x4 2)  Find the derivative of Sums and Differences a. Let f(x)=6x+7 and g(x)=­2x­3 Find the derivative of [f(x) + g(x)]. b. Let f(x)=4x­2 and g(x)=7x­4 Find the derivative of [f(x) – g(x)] 3) Find the derivative of the polynomials. 3 a. f(x)=6x b. f(x)= ­5x 5 c. f(x)= 3x + 4x ­ 5x  2 x d. f(x)= 4  + 6           7 5  √ x e. f(x)= 3x ­ 5  +  x 4)  Find f ‘(x), f ‘(3), and f ‘(5) for f(x)= 3x  + 5x – 2 5) Find the equation of the line tangent to the curve at x=3 for the equation 3 2  f(x)=4x +6x ­2x+7 6) Find the derivative. a. f(x)= 8 x x b. f(x)= e c. f(x)= 4e ­3x d. f(x)= x + 6 ln(x) 7)  Find the equation of the line tangent to the graph f(x)= ln(x)  at x=3. 8)  Find the derivative using the chain rule. a. f(x)= ln(6t) b. f(x)= e ­5x 3 e 4x c. f(x)=  2 d. f(x)= (3x+7) 5 e. f(x)= 2(4x+1) 2  f. f(x)= 5 ln (2x + 5) √(3+4e ) 3 x g. f(x)=  9)  The annual world soybean production, W=f(t) in million tons, is a function  of ‘t’ years since the start of 2000. a. Explain f(8)= 253 and f ‘(8)= 17. b. Calculate the relative rate of change at t=8 10)  Find the derivative of the equations using the product rule. 2 5 a. f(x)= x  (2x + 7) b. f(x)= 3x ln(x  + 2) c. f(x)= x ln(x) 3­5x d. f(x)= x e 7e 6 x e. f(x)=  x 11)  Find the derivative of the equations using the quotient rule. 3x 4 a. f(x)=  3 x +6 7 b. f(x)=  3+e 3 x 2 ex c. f(x)=  4 2 x x d. f(x)=  x e 1−x e. f(x)=  1+x Answer Key: 1)   a. f ‘(x)= 0 b. f ‘(x)= 7 8 c. f ‘(x)= 9 x −1 45 d. f ‘(x)=  x 4 −5 e. f ‘(x)= ­4 x 2) a. f ‘(x)= 4 b. f ‘(x)= ­3 3)   a. f ‘(x)= 18 x2 x4 b. f ‘(x)= ­25 2 c. f ‘(x)= 9 x +8x−5 1 x d. f ‘(x)=  2 −1 x − x −7x −2 e. f ‘(x)= 15 2 4)   f ‘(x)= 6x + 5 f ‘(3)= 23 f ‘(5)= 35 5)  y = 142x + 0.38 6)   a. f ‘(x)= ln(8) 8 x ex b. f ‘(x)=  −3 x c. f’ ‘(x)= ­12 e 6 d. f ‘(x)= 2x +  x 1 x 7) y =  3  + 1.0986 8)   6 a. f ‘(x)=  6x −5x b. f ‘(x)= ­5 e 3 e4x x2 c. f ‘(x)=  (12 ) d. f ‘(x)= 2(3x + 7)(3)    or    f ‘(x)= 18x + 42 4 e. f ‘(x)= 40 (4 x+1) 20x f. f ‘(x)=  2x +5 −1 e3 x2 3+4 ¿ g. f ‘(x)= 6 e ¿x 9)   a. In 2008, the soybean population production was 253 million tons.  In  2008, the soybean production was increasing at a rate of 17 million  tons per year. b. RROC= 6.7% per year 10)    5 2 4 a. f ‘(x)= 2x (2x+7)  + 10 x (2x+7) 3 9x 3 b. f ‘(x)= 3ln( x + 2) +  3 x +2 c. f ‘(x)= ln(x) + 1 3−5 x 3−5 x d. f ‘(x)=  e +  5xe 42e 6x 7e 6 x 2 e. f ‘(x)=  x  +  x 11)    6 3 3x +72x a. f ‘(x)=  (x +6) 2 3 x 21e b. f ‘(x)=  3 x2 (3+e ) 4 2 2x ¿ ¿ c. f ‘(x)=  5 x2 3 x2 4x e −8x e ¿ 1−x d. f ‘(x)=  x e −2 e. f ‘(x)=  (1+x) 2  


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