Math 1325 Test 3 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the location and value of each relative etremum for the function. 1) Identif the intervals where the function is changing as requested. 2) Increasing Find the largest open interval where the function is changing as requested. 3) Decreasing = 1 2 + 7 Determine the location of each local etremum of the function. 4) f() = 3-1 2 2-6 + 4 Use the first derivative test to determine the location of each local etremum and the value of the function at that etremum. 5) f() = 2-2 + 1-5 1
Solve each problem. 6)The cost of a computer sstem increases with increased processor speeds. The cost C of a sstem as a function of processor speed is estimated as C = 7S2-5S + 1800,where S is the processor speed in MHz. Find the processor speed for which cost is at a minimum. 7)The velocit of a particle (in ft/s) is given b v = t 2-6t + 2, where t is the time (in seconds) for which it has traveled. Find the time at which the velocit is at a minimum. Evaluate f"(c) at the point. 8) f() = (2-3)(3-4), c = 1 9) f() = e-, c = 0 Solve the problem. 10)Find the velocit function v(t) if s(t) = -3t3-5t2 + 4t + 5. 2
s is the distance (in ft) traveled in time t (in s) b a particle. Find the velocit and acceleration at the given time. 11) s = 7t3 + 3t2 + 3t + 8, t = 3 Find the coordinates of the points of inflection for the function. 12) f() = 3 + 272 + 240 + 703 Find the largest open intervals where the function is concave upward. 13) f() = 3-32 - 4 + 5 Find all critical numbers for the function. State whether it leads to a local maimum, a local minimum, or neither. 14) f() = 3-32 + 3-2 The rule of the derivative of a function f is given. Find the location of all local etrema. 15)f'() = ( + 1)( - 2)( - 3) Solve the problem. 16)When an object is dropped straight down, the distance in feet that it falls in t seconds is given b s(t) = -16t2, where negative distance (or velocit) indicates downward motion. Find the velocit and acceleration at t = 7. 3
Find the absolute etremum within the specified domain. 17)Minimum of f() = 3-3 2 ; [- 0.5, 4] Solve the problem. 18)From a thin piece of cardboard 30 in. b 30 in., square corners are cut out so that the sides can be folded up to make a bo. What dimensions will ield a bo of maimum volume? What is the maimum volume? Round to the nearest tenth, if necessar. 19)If the price charged for a cand bar is p() cents, then thousand cand bars will be sold in a certain cit, where p() = 142 -. How man cand bars must be sold to maimize 28 revenue? (Remember that revenue is price times number sold.) Sketch the graph and show all local etrema and inflection points. 20) f() = 23 + 152 + 24 24 12-8 -4 4 8-12 -24 2 21) f() = 2-25 3 2 1-10-8-6 -4-2 2 4 6 8 10-1 -2-3 4
Sketch a graph of a single function that has these properties. 22) (a) defined for all real numbers (b) increasing on (-3, -1) and (2, ) (c) decreasing on (-, -3) and (-1, 2) (d) concave upward on (-, -2) and (1, ) (e) concave downward on (-2, 1) (f) f'(-3) = f'(-1) = f'(2) = 0 (g) inflection point at (-2, 0) and (1, 1) 5
Answer Ke Testname: MATH 1325 T3RS14 1) (-3,-1), (-1,2), (2,1) 2) (-2, -1) (2, ) 3) (0, ) 4) Local maimum at -2; local minimum at 3 5) Local maimum at (1, 0); local minimum at (9, 16) 6) 0.4 MHz 7) 3 s 8) f"(1) = -6 9) f"(0) = 1 10) v(t) = -9t2-10t + 4 11) v = 210 ft/s, a = 132 ft/s2 12) (-9, 1) 13) (1, ) 14) No local etrema 15) Local maimum at 2; local minima at -1 and 3 16) Velocit = -224 ft/sec; acceleration = -32 ft/sec2 17) (2, -4) 18) 20 in. b 20 in. b 5 in.; 2000 in.3 19) 1988 thousand cand bars 20) Local ma: -4,16, min: -1,-11 Inflection point: - 5 2,5 2 24 12-8 -4 4 8-12 -24 6
Answer Ke Testname: MATH 1325 T3RS14 21) No relative etrema Inflection point: (0, 0) 3 2 1-10-8-6 -4-2 2 4 6 8 10-1 -2-3 22) 7