Answers edited by Stacey R.

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• How do you differentiate the given function? F(y) = (#1/y^2# - #3/y^4#)(y + 5y^3)
  
• On what interval is f concave upward? f(x)=xln(x)
  
• What is the equation of the tangent line and normal line to y = 2x#e^x# at (0, 0)?
  
• A sheet of cardboard 3 ft by 4 ft will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. What will be the dimensions of the box with the largest volume?
  
• On what interval is the function f (x) = x^3 e^x increasing?
  
• How do you solve the AP Calculus AB 2013 Free Response question #2? http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_calculus_ab.pdf
  
• How do you differentiate # f(x)=(x^-2+5x)(x^3+4)# using the product rule?
  
• A box with an open to is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. find the largest volume that such a box can have?
  
• How do you differentiate the equation? #F(y)= (1/y^2 + 3/y^4) (y+5y^3)#
  
• A piece of wire 60 cm in length is cut into two pieces. The first piece forms a rectangle 5 times as wide as it is long. The second piece forms a square. Where should the wire be cut to? 1)minimize the total area 2)maximize the total area
  
• Find points on the curve y={2x^3+3x^2-12x+1} where the tangent is horizontal?
  
• Hw do you prove that the d/dx (secx) = sec x tan x ?
  
• What is the equation of the tangent line to the curve y = 2xsin(x) at point (pi/2, pi)?
  
• Question #1561c
  
• Given information about the fill and empty rate, how do I find the volume after t minutes?
  
• What is the derivative of #y = (x^2+4x+3)/sqrtx#?
  
• Construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2. Volume of the box is 50 ft3, what are the dimensions that will MINIMIZE the Cost?
  
• How do I graph the rational function: #y=-6/x+4#?
  
• Build a rectangular pen with three parallel partitions (meaning 4 total sections) using 500 feet of fencing. What dimensions will maximize the total area of the pen?
  
• How do you differentiate the equation?
  
• Find the equation of the tangent line to the curve at the given point?
  
• How do I evaluate #d/dx \int_5^(x^4) \sqrt{t^2 + t} dt#?
  
• How do you evaluate #d /dx \int_[x]^{x^4} sqrt{t^2+t} dt#?
  
• How do I graph the function: #y=(2x)/(x^2-1)#?
  
• A farmer w/ 750ft of fencing wants to enclose a rectangular area then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
  
• Find all points where the tangent line is horizontal: #x^2+xy+y^2=1#?
  
• How do you solve #int_0^2 x^4+5x dx#?