An isosceles triangle whose base is the interval from (0,0) to (c,0) has its vertex on the graph of f, where f(x)=12-x^2 for x is greater than or equal to 0 and f(x) is greater than or equal to 0. For what value of c does the triangle have maximum area? Justify your answer.

Consider the relation defined by the equation tan y = x + y for x in the open interval 0 is less than or equal to x which is less than 2pi
(a) Find dy/dx in terms of y
(b) Find the x- and y- coordinate of each point where the tangent line to the graph is vertical
(c) Find d^2y/dx^2 in terms of y

Use the definition of the derivative to find f '(x) given
f(x)=^/¯x
Write an equation of the line tangent to the curve at the point P(-1, 7). Express the answer in the form ax + by = c.
y= 5/x^2-2/x^3
Write the equation of the line tangent to the curve at the point P where x = 4. Write the equation in the f

All solutions must be detailed and the final answers simplified. Show all work!
1. Differentiate the given function. Simplify your answer.
2. Differentiate the given function. Simplify your answer.
3. Differentiate the given function. Simplify your answer.
4. Find the equation of the line that is ta

3. Parcel Post
A firm wishes to use the services of a parcel delivery company to transport a cylindrical package. The package has volume V=pr2l, where l is the length of the package in metres and r is the radius of the circular end in metres. The parcel delivery company will only transport parcels provided that the sum of the

Rules andApplications of the Derivative
--------------------------------------------------------------------------------
1. Use the Product Rule to find the derivatives of the following functions:
a. f(X) = (1- X^2)*(1+100X)
b. f(X) = (5X + X^-1)*(3X + X^2)
c. f(X) = (X^.5)*(1-X)
d. f(X) = (X^3 + X^4)*(30

The U. S. Postal Service will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 108 in. What dimension will give a box with a square end the largest possible volume? Show your work.

1. Determine dy for each of the following relations.
dx
a) 9x2-16y2=1
b) y3+5xy+x3=1
2. Determine the slope of the curve 8x3+3xy+8y3=19 at the point (1,1).
3. Determine the equation of the tangent to the given curve at the given point.
x2-y2-x=1 at (2,1)
4. Determine the equat

A box is made from a sheet of metal that is 8 meters by 10 meters, by removing a square from each corner of the sheet and folding up the sides. Find the width of the square to removed in order to have a box of maximumvolume.