ftp Ch. 5 i A particle moves along the x-axis so that, at any time t> 0 , its acceleration is given by a(t) = 61 + 6 . At time 1=0, the v e l o c i t y of the particle is -9, and its position is -27. A) B) C) Find v(t), the.-Y€tocity of the particle at any time t > 0 For what values of t>0 is the particle moving to the right? Find x(t), the position of the particle at any. time t> 0 RR 2. Determine a, b, c, and d so that the graph of y = ax3 + bx 2 * cx + d nas a point O f inflection at the origin and a relative maximum at the point (2,4). Sketch the graph flp 3: The volume V of a cylinder is increasing at the rate of 307T cubic units per second. At the instant when the radius r' of the cylinder is 2 units, its volume is 12TT cubic units and the radius is increasing at 1/3 units per second. A) B) C) At the instant, when the radius of thecvi'«* r is 2 units, what is the rate of change of the area of its base. At the instant when the radius of thecyW^is 2 units, what is the rate of change of its height h. At the instant when the radius of the c^^ris 2 units, what is the instantaneous rate of change of the area of its base with respect to its height h? flP 4. At time 1=0, a train is going at a velocity of 1000 meters per minute. The train is slowing down with a negative acceleration that is directly proportional to time t. This brings the train to a stop in 5 minutes. " A) Write an expression for the velocity of the train at time t. B) What is the total distance traveled by the train in that 5 minute interval? ~ 5 A function f following 3 i) 11) is defined for all real numbers and has the properties f(1) = 5 f(3) = 21 for all real values of a and b f(a+b) - f(a) = kab + 2b2 where k is a fixed real number independent of a and b A) use e=1 end b=2 to find the value of k B) C) Find f(x) Find f(3) ftP £^.5 6. f(x) = x 3 - 7 x + 6 Find the average value of y that satisfies the mam Value Theorem on [1,31 7. A particle moves along the x-axis so that, at any time t>0, its acceleration is given by a(t) = 81-8' At time 1=0, the velocity of the particle is -12 A) Find v(t), the velocity of the particle at any time t> 0 B) For what values of t> 0 is the particle moving to the left? C) Find x.(l), the position of the particle at any time t> 0, if the position is 14 when 1=3 . . 11 8 f(x) =4 x-2 x2 A) Domain B) Range C) For what values of x is the function continuous? D) For what values of x is the derivative continuous? 5 A particle moves along the x-axis so its velocity at any time t>0 is given by v(t) = zt2 -»-4t-48 A) B) C) Find acceleration a(t) Find all values of t for which the particle is at rest Find the postion x(t) if x(0) = -1 Mi. 8 ID. ft - A B) PlwJ X-;N~f< o c)Ru^. x * y •1 H -5 5 ftP OL\\J ^ X- Ch. 5 # 5 A particle, initially at rest, moves along the y-axis so that its acceleration at any time i £ 0 is given by a(/) = 12r2 — 4. The position of the particle when r =» 1 is x(\) « 3. (a) Find the values of r for which the particle is at rest. (b) Write an expression for the position *(/) of the particle at any time t £ 0. (c) Find the total distance traveled by the particle from / » 0 to / = 2. 12.. . Let / be the function given by f (x) = v.v 4 - 16.v2 . (a) Find the domain of/. (b) Describe the symmetry, if any, of the graph of /. (c) Find/'(jc). (d) Find the slope of the line normal to the graph of / at x = 5. nn Mr Ix-il -5 ^CH ^/f / ™ / j p ' S> - ui ' / - a C71 U /7/V/J ' ^ - g /k7 yr<( si \]U (i/ 5/ sf / (V ^o \j

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