M 145 Lecture Notes - Lecture 2: Power Rule

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pearmouse897

21 Sep 2016

School

University of Hartford

Department

Mathematics - A&S

Course

M 145

Professor

Hadad Alan

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Document Summary

Function: relationship between an independent and dependent variables. Derivative: rate of change (slope) at any point of a line. Derivative can be represented by: dy/dx, y", or f"(x) Constant of integration y = 6x2 + 3x + 1 vs y = 6x2 + 3x +2. The original functions are different due to the constant, however when taking the derivative, the answer is the same for both: y = 12x + 3. This creates a dilemma when going the opposite direction. When integrating a function, you must always account for the constant that may or may not be in the function by adding a + c. If there is a constant multiplied by the function, you can move it outside the integral and multiply after o. If there is more than one function inside an integral separated by addition or subtraction, you can separate them o.

Related Questions

Help with 38,42,47,55 please

Mnct 60. fx)-3x3x 61, f(x) = x.(x-z? Applications of Differentiation 212 CHAPTER 3 Find all critial hunber 35. 40, g(Î¸)-48-tane 39. F(x)-x""(x-4): 41. f)-2 cos8 + sino 63. Between 0Â°C and 30Â°C, the volume V Gn of I kg of water at a temperature T is 43-44 A formala for the derivartive of a function f'is given. How many critical numbers does f have? V-999.87-0.06426T0.00850437 Find the temperature at which water has its m APTE - 6x + 10 64. An object with weight W is dragged along a h attached to the o by a force acting along a rope rope makes an angle Î¸ with the plane, then the 45-56 Find the absolute maximum and absolute minimurn values the force is Î¼ sin Î¸ + cos Î¸ of f on the given interval. 45. fx)-12+4x -. [0,S] 46. fix)-5+54x-2x. (0,4) å¸f(x)-2x,-3x1-12x + 1, [-23] where Î¼ is a positive constant called the coefficie and where 0 Î¸ Ï/2. Show that F is minimize 65. The water level, measured in feet above mean sea l Lake Lanier in Georgia, USA, during 2012 can be im the function L()-0.01441,, 50. f)- 4). [-2,3] 51.)(02.4) 52. x)-+T -0.4177,2 + 2703t + 1060. where t is measured in months since January 1,201 when the water level was highest during 2012. 66. On May 7, 1992, the space shuttle Endeavour was laun on mission STS 49, the purpose of which was to install perigee kick motor in an Intelsat communications satellit The table gives the velocity data for the shuttle between l and the jettisoning of the solid rocket boosters. (a) Use a graphing calculator or computer to find the cubi S4. ft)- 0.2 pol ymomial that best models the velocity of the shuttle interval r e [o, 125). Then graph this polynom acceleration of the shuttle and usew ss fc)-2 cos+sin 2t, [o, -/2 56. f(t)-' + cot('/2), [Ï/4.7v/4] 57. If a and b are positive bumbers, find the maximum value 58. Use a graph ximum and minimum values of the to estimate the critical numbers of fx)-II+5xcorect i e decil place 59-62 (a) Use a graph to estimate the absolute (b) Use calculus to find the exact 0 maximurm and 0 185 319 447 values of the function to two decimal places. minimum maxirsum and minimum values 20 32

M 145 Lecture Notes - Lecture 2: Power Rule

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