Question

1. Consider the equation below. (If an answer does not exist, enter DNE.)

f(x) = e^2x + e^−x

(b) Find the local minimum and maximum values of f.

local minimum value

2. A particle is moving with the given data. Find the position of the particle.

a(t) = 13 sin(t) + 6 cos(t),    s(0) = 0,    s(2π) = 10

3. Find the area of the largest rectangle that can be inscribed in the ellipse

x²

a²

+

y²

b²

= 1.

4. Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle.

height:

5.

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1536 cm², find the dimensions of the poster with the smallest area.

width	cm
height	cm

6. A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

(b) How much wire should be used for the square in order to minimize the total area?

Answer 1