Math 25O Test 2 (Hour Exam : perfect = 45) given Spring 2017 Credit given in proportion to the clarity of your WORK You need not evaluate anything beyond a point where a calulator is necessary 



[1]  (Handout #1: n,d,p,k,j)(1 pt each) If f(x) = 3x + 2 and g(x) = x^{2}  1, enter integers (such as 7, 1, 0, or 4) to find: 
(a) g( 1 ) = 


(b) f(x + 1) = 


(c) g(x  1) = 


(d) f(g(x)) = 


(e) f(f(x)) = 

[2]  (a)(Pg 42 #49)(3 points) Students at UWJanesville may either preregister on the web before 17 January 2006, or register in person after 8 A.M. on that date. The registrar handles 35 students per hour in person, and by noon of 17 January 2006, a total of 360 students had been registered, including those who preregistered before 17 January 2006. Let N be the total number of students registered as of x hours after 8 A M. on 17 January 2006. :  

(b)(Pg 26 #31)(2 pts) Find the two points at which the graphs of [ y = x^{2} ] and [ y = 3x  2 ] intersect. Display algebra work as you solve this problem. Check by substitution or graphing calculator output do NOT count as algebra  

[3] 



[4] 



[5] 
(Pg 186 part of #1) Use the LIMIT METHOD to find f '(x) if
f(x) = x^{2}  3x + 1. The answer is that f '(x) = 2x  3, but DO NOT USE "QUICKIE" RULES (such as the power rule) to find f '(x). Also, you must correctly use limit notation at least twice for full credit (see problem [4] above as an example). This is the only exam problem requiring the limit method to find f '(x). 
[6] 

For the remaining problems on this test, you may use any rule or method for full credit, including the product and quotient rules. The limit method should be avoided because it would be very difficult to use properly. Showing your methods clearly may save you points. 
[7]  (Pg 156 #35 exponents changed, difficulty the same) Find f '( x) if f(x) = (x + 2)^{9}(2x  1)^{8}  

[8] 
(Pg 181 #11) Use implicit differentiation to find
y' (the first derivative of y) if x^{3} + y^{3} = xy . Thus, do NOT first solve for y (it would be hard), but rather : differentiate both sides of the given equation. Your answer to [8] must be an equation with y ' alone on the left side ; the right side of your answer will contain the variables x and y, but must not contain y' . 
[9]  (Pg 143 #43 one number changed) Find y', y", and y''' if y = 2x^{5}  4x^{3} + 9x^{2}  6x  2. 