Problem 1 (15 Points): A farmer has 300 linear feet of fence to encompass the two adjacent pastures shown in the sketch to the right.

Using the variable names shown in the sketch, determine the values of x and y in order to maximize the enclosed pasture area.

computing the first derivative:

Problem 2 (15 Points): Find all roots of f(x). Include a legible graph of f(x) labeled with the roots. One of the roots is r₁ .

graph the function in R

Using my root finding function on my calculator using some initial guesses:

using division with:

yields:

using the quadratic equation to find the other 2 roots yields:

Answer(s):

Problem 3 (15 Points): Determine the domain and range of the composite function h(x). Include a legible graph of h(x).

Comments:

domain:

range:

domain:

(since ln(0) is undefined and ln(1) = 0)

range:

(since e⁰ = 1 yielding ln(1) = 0 which causes the h(x) denominator = 0)

domain:

range:

and

Problem 4 (15 Points): Accurately estimate the SHM (Simple Harmonic Motion) equation h(t) shown in the graph below. Please graph your equation on your calculator to confirm it's exactness.

Since:

Amplitude = 4

Bias = - 2

T = 6, so

Use the sine curve with no apparent phase shift (f)