Semester Exam Review Part No Calculators d d. For the graph shown, at which point is it true that < 0 and --t > o? AA B.B C.C D.D E.E. Line L is normal to the curve defmed by xy - y = 8 at the point (,). The slope of the line L is? 0 8 8 A B. C.- D.- E.- 8. Find the value ofx at which the graph of y =! + ~ has a point of inflection. X A. C. 4 D.6 E. 8.. x+ x x-00x -4x +x 4.Fmd hm A B. C. D. - 4 E. - 5. Let y be a differentiable function with dy > 0 for all x. For which of the following values ofy is it d d true that -y = 8-lny? I. y=- II. Y = III. Y = 4 A I only B. II only C. III only D. I and II E. II and III 6. Let f(x) = cost 7tX ) Find f'g)..jt A-..Jrt B...Jt C.O D.--- E. -t 7. Let f(x) = tan- (x). Find '() t A.- B.- C.- E. undefined 5 D. -
Semester Exam Review Part No Calculators. For the graph shown, at which point is it true that dy < 0 and d ;, > O? A.A B.B C.C D.D E.E. Line L is normal to the curve defmed by xy - y = 8 at the point (,). The slope ofthe line L is? 0 8 8 A. - B. C.- D.- E.- 8. Find the value of x at which the graph of y =.!.. + -J; has a point of inflection. x A. C. 4 D.6 E. 8. d l' x+ x 4. Fm m x-+oox -4x +x A.- B. C. D. -- E. - 4 5. Let y be a differentiable function with dy > 0 for all x. For which ofthe following values ofy is it d d true that - y = 8-In y? A. I only B. II only 6. Let i(x) = costm ). Find f'g) A.--Jn 7. Let /(x) = tan-i (x). Find /'() I. y= C. III only C.O II. Y = D. I and II -Jn D.---' III. Y = 4 E. II and III E. - n n A. B. 5 C. D. -J E. undefined
8. The graph of a function y =f(x) is shown above. Which ofthe following are true for the function f(x)? I. f'() is defmed II. lim f(x) = linl f(x) x-+ x- III. f(x)<o forallxon (-,) ~ I A. I only B. II only C.IIIonly D. II and III c E. all three 9. Let f(x) = ex - x - 4x + 5. Then f has a local minimum at x =? A.- B. --c.- D.l. 0. The acceleration ofa particle moving along the x-axis is a(t) = t -0. At t = 0, the velocity is. At t =, the position is x = 4. Find the position at t =. A. B.4 C.5 D.6 E. 7 x. Find an equation ofthe line tangent to the graph of y = at x =. x -6 A.5x+y=8 B.5x-y= C.5x+y=4 D.x-5y=- E. x+ y=6 (x+ h) _x. Letg(x) = lim. For what value ofx does g(x) =? h-d h A. x = B. x= C. x= D. x=4 E. x=5. Let f be a differentiable function of x that satisfies f () = 7 and f (4) =. Which ofthe following conditions would guarantee that the tangent line at x = c is parallel to the secant line joining (,f(i)) to (,f(4))? A. f(c) = ~ B. f(c)=5 C. f'(c) =-~ D.f'(c)=_4 E. f'(c) = 4 4 4. Let f(x) = j -x. Which statement about this function is false? A. The function has one inflection point. B. The function is concave up for x > 0 C. The function has two relative extrema D. The function is incr~asing for values of x on (-,) E. The function has a relative minimum at x =
x, -x-6 5. Let /(x)be a continuous function that is defined for all real numbers x. If / (x) =--- x -5x+6 when x - 5x + 6;! 0, what is /()? AO B.l C. D.4 E.5 6. Find the derivative of cos (x) A -sin (x) B. 6cos (x) C.6cos (x)sin(x) D. - cos (x)sin(x) E. - 6cos (x)sin(x) 7. Let / be a twice differentiable function whose derivative /'(x) is increasing for all x. Which of the following must be true for all x? I. /(x»o II. /'(x) >0 III. /"(x) >0 A I only B. II only C. III only D. I and II E. II and III 8. The function /(x) = x - 6x + 9x - 4has a local maximum at A x=o B. x = c. x= D. x= E. x=4 9. Let /(x) = g(h(x)), where h() =, h'() = 4,g() = and g'() = 5. Find /'(). A 6 B. 8 C. 5 D.0 E. Not enough info to detennine. 0. The velocity of a particle moving along a straight line is given by v(t) = x - 4x. Find an expression for acceleration ofthe particle. A x-4 B. 6x-4 C. x -4x E. x -4. Find the rate ofchange ofthe function y = x - 4x on the closed interval [0,4] A8 B. C.4 D. E.48 Ok, you can use your calculator on the rest of these problems.. Let / be a differentiable function that is defined for all real numbers x. Use the table below to estimate /'(.5). x..4.5.6.7 /(x).69.96 4.5 4.56 4.89 A 0. B..8 c..7 D..0 E.6.0
x - 4, for xt..... Let f(x) =. WhIch ofthe followmg are true statements about this function? {6x-5, for x > I. limf(x) exists II. limf'(x) III. f'(l) exists x-i x-i A None ofthese B. II only C.IIlonly D. II and III E. All three. 4. Two particles are moving along the x-axis. Their positions are given by xl (t) = t - 5t - 7 and X(t) = sin(t) respectively. If al (t) and a(t) represent the acceleration functions ofthe particles, find the numbers of values of t in the closed interval [0,5] for which al (ty= a(t). AD B. C. D. E. 4 or more 5. The function f(x) = ex - x has how many critical points? AD B. c. D. E. 4 or more 6. A dog heading due north at a constant speed of meters per second trots past a fire hydrant at t = 0 sec. Another dog heading due east at a constant speed of meters per second trots by the hydrant at t = sec. At t = 9 sec, the rate of change ofthe distance between the two dogs is A. m/s B..6 m / s C. 4.0 m / s D. 4.4 m/s E. 4.8 m/s (lnt) ft% t sec 7. Suppose air is pumped into a balloon at a rate given by r( t) = for t ~ sec. If the volume of the balloon is.ft at t = sec, what is the volume ofthe balloon at t = 5 sec.? \ A.7ft B..0ft c. 0ft D..6ft E..9ft 8. Find the approximate value of x where f(x) =x - -Jx+ has its absolute minimum. A - 4.5 B. - c. 0 D. 0.5 E..5 9. The graph of y =f'(x) is shown. Which ofthe following statements about the function f(x) are true?,/ I. f(x) is decreasing for all x on a and c. II. The graph of f is concave up for all x between a and c III f(x) has a relative minimum at x=a A I only B. II only C. III only D. I and III E. All three