A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of....
Class XII_ Applications of Derivatives_Maxima-Minima Q275 A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window. Previous recorded questions and their links: ROCOQ Q13: The volume of a cube is increasing at the rate of 8 cm3/s • The volume of a cube is increasing at the ... Q17: A balloon, which always remains spherical on inflation: • A balloon, which always remains spherical ... Q25: The volume of a spherical balloon is increasing at: • The volume of a spherical balloon is incre... Q27: The length x of a rectangle is decreasing at the rate of: • The length x of a rectangle is decreasing ... Q30: The total cost C(x) in Rupees, associated with the production: • The total cost C(x) in Rupees, associated ... Q34: The amount of pollution content added in air in a city: • The amount of pollution content added in a... Q35: A ladder 5m long is leaning against a wall: • A ladder 5m long is leaning against a wall... Q36: The side of an equilateral triangle is increasing: • The side of an equilateral triangle is inc... Q39: A kite is moving horizontally at the height of 151.5 meters: • A kite is moving horizontally at the heigh... Q52: Water is dripping out from a conical funnel of semi-: • Water is dripping out from a conical funne... Monotonicity (Increasing & Decreasing Functions) Introduction: • Monotonicity (Increasing & Decreasing Func... Q70: Prove that the function f(x)=x^3-x^2+12x-18… • Prove that the function 𝒇(𝒙)=𝒙^𝟑−𝒙^𝟐+𝟏𝟐𝒙−𝟏... Q64: Show that the function given by 𝒇(𝒙)=𝟕𝒙−𝟑 is strictly increasing on R. + Q68: Show that the function 𝒇(𝒙)=𝒙^𝟑−𝟑𝒙^𝟐+𝟔𝒙−𝟏𝟎𝟎 is increasing on R. • Show that the function given are strictly ... Q105: Find the intervals in which the function f(x)=x^2–4x+6 are increasing or decreasing. • Find the intervals in which the function 𝒇... Q113: Find the intervals in which the function f(x)=2x^3–9x^2+12x+15are increasing or decreasing. • Find the intervals in which the function f... Q118: Find the intervals in which the function f(x)=3/10 x^4-4/5 x^3-(3〖x)〗^2+36/5 x+11 are increasing or decreasing. • Find the intervals in which the function 𝒇... Q133: Find the intervals in which the function f(x)=sin3x, x ϵ[0,π/2] are increasing or decreasing. • Find the intervals in which the function 𝒇... Q134: Find the intervals in which the function f(x)=sinx+cosx, 0≤x≤2π are increasing or decreasing. • Find the intervals in which the function 𝒇... Q140: Find the intervals in which the function f(x) =log(1+x)–2x/(2+x) are increasing or decreasing. • Find the intervals in which the function f... Maxima - Minima Q270: Manufacturer can sell x items at a price of rupees (5-x/100): • Manufacturer can sell x items at a price o... Q276: A given rectangular area is to be fenced off, in a field : • A given rectangular area is to be fenced o... Q279: A cuboidal shaped godown with square base is to: • A cuboidal shaped godown with square base ... Q282: If length of three sides of a trapezium other than : • If length of three sides of a trapezium ot... Q271: Show that of all the rectangles inscribed in a given circle, the square has the maximum area. • Show that of all the rectangles inscribed ... Q306 The sum of the surface areas of a rectangular parallelopiped (cuboid) with sides x, 2x and x/3 and a sphere is given to be constant. Prove that the sum of the volumes is minimum, if x is equal to three times the radius of the sphere. Also, find the minimum value of the sum of their volumes. • The sum of the surface areas of a rectangu... Q308 Of all the closed cylindrical cans (right circular), of a given volume of 128𝝅 cubic centimetres, find the dimensions of the can which has the minimum surface area? • Of all the closed cylindrical cans (right ... Q310 Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the Sphere. • Prove that the volume of the largest cone ... Q312 Show that the right circular cone of least curved surface and given volume has an altitude equal to √2 time the radius of the base. • Show that the right circular cone of least... Q1 Find the rate of change of the area of a circle with respect to its radius r, when r = 3 cm • Find the rate of change of the area of a c... Q2 Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm. • Find the rate of change of the area of a c... Q7 If the area of circle increases at a uniform rate, then prove that the perimeter varies inversely as the radius. • If the area of circle increases at a unifo... Q8 A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing? • A stone is dropped into a quiet lake and w... Q273: • Show that of all the rectangles of given a... Q274: • Find the area of the greatest rectangle th... #cbse #icse #boards #8th #9th #10th #foundation #competition #iit #jee #Advanced #mains #ntse #olympiads #exams #examination #achiever #topper #zenith #zenithinstituteofmathematics #indersir #ludhiana #modelgram #bestmathscoaching #besttutorials #besttuition #bestinludhiana #mathtricks #viii #ix #x #xi #xii #important #excellent #question #aod #derivatives #chainrule #Increasingfunctions #decreasingfunctions #tangentsandnormals #monotonicity #maximaminima #absolutemaxima #absoluteminima #localmaxima #localminima #approximations
