AutoSave 0 Off) 0 B C TestZ Review Exercises Calculusl Fall 2021 7 Word A Priscilla Sanchez File Home Insert Draw Design Layout References Mailings Review View Help I3 Share l3 Comments MATH 2413 Calculus 1 Review Problems for Exam #2 Fall 2021 1. (3) Shown below are the graphs of four functions, f1,f2,f3, and f4. 3 y = 1100 y = f2(x) y = f3(x) For each function, identify which of the following is the graph of its derivative. Paqe1of2 316words [1 :D:Focus [:59 7417+ 130% Search A Priscilla Sanchez X AutoSave . Off H Test 2 Review Exercises Calculus 1 Fall 2021 - Word Z PST Comments File Home Insert Draw Design Layout References Mailings Review View Help Share (b) Shown below is a graph showing the position s of an object (in meters) at time t (seconds) as it moves along a line. Sketch a graph of the object's velocity function. 2.5 2 1.5 1 0.5 5 7 8 9 Focus + 140% Page 1 of 2 316 words 3:43 AM 9 P w O 77OF Clear 10/4/2021AutoSave . Off H Test 2 Review Exercises Calculus 1 Fall 2021 - Word Search A Priscilla Sanchez Z PST X File Home Insert Draw Design Layout References Mailings Review View Help Share Comments 2. Find the derivative of each function. a. g(t) = sin(6t3 + 8t2) 4x2 - 3x +2 f. f ( x ) =- 7x3 - 5x2 b. h(x) = 4Vx+- 8 Vx g. y = In(tan (x)) c. f(x) = 5 csc (x) + xsec(x) h. g(x) = e2x In (x) tan-(x) d. y = i y = cos(5x7 - 12x) 1 + x2 e. y = e8 cos(x2) j. y = 6 sin-1(3x2) 0 3. Find the indicated derivative value for the given function. a. f (x) = -2, f'(2) 5 c. h(x) = 7x+ cos-1(x), h'(0) b. g(x) = In (x2 + 1), g'(1) d. f (x) =3 cot(2x), f' (*) Page 2 of 2 316 words Focus + 160% 3:44 AM O 9 P w 77OF Clear 10/4/2021AutoSave 0 Off 0 B C TestZ Review Exercises Calculusi Fall 2021 7 Word , 75' : A Priscilla Sanchez PT. File Home Insert Draw Design Layout References Mailings Review View Help I3 Share l3 Comments 4. Find the second derivative of each function. a. f(x) = 7x3 2x2 + 5x + 11 (b)y = 65x2 5. Find the equation of line tangent to the graph of the given function at the specified point, writing your result in slopeintercept form y = ax + b. a. y = 4x3 + 2x 1 at (0, 1) b. g(x) = x/(x2 + 4) at the point where x = 1. 6. a. A model rocket is fired vertically upward from the ground, and its heights (in meters) above the ground it seconds after its launch is given by s(t) = 4.9t2 + 120t. (i) Find the velocity of the rocket 5 seconds after being launched. (ii) Is the rocket going up or down 5 seconds after being launched? (iii) Find the acceleration of the rocket 5 seconds after being launched. (iv) At what time(s) is the rocket at rest? 2t t2+50 Find the rate of change of the number of bacteria at 10 hours; is the number of bacteria increasing or decreasing at that instant in time? b. The number of bacteria in a culture is N(t) = 4000 ( 1 + ) where t is measured in hours. 7. Use logarithmic differentiation to find the derivative of each function. a. y = (x2 + 16)COS(x) b. y = x59: 4 ) Paquof2 316words [1 :njrocus Fe 7++ 160% 3:44 AM J 77=F Clear .\\ la J2 E ram/2021 D