Please show your work for every single one..thats more important..thanks. Must d
ID: 2833265 • Letter: P
Question
Please show your work for every single one..thats more important..thanks. Must do all ,,thanks.
1) Find the critical number of this function.
2) Find the intervals of increasing and decreasing.
3) Find the relative maximum and relative minimum.
4) Find the interval of concavity.
1) Find the domain.
2) Find x,y-intercepts of "f"
3) Find the vertical and horizontal asymptotes of "f"
4) Find the critical numbers of "f" if any
5) Find the interval of increasing and decreasing
6) Find the relative maximum and relative minimum of "f" if they exist.
7) Find the intervals of concavity
8) Sketch the graph "f"
Find the dimensions of a rectangle of area 144 sq. ft that has the smallest possible perimeter
Explanation / Answer
A = x * y
144 = x * y
(144 / x) = y
p = 2x + 2y
p = 2x + 2 * (144/x) ====> derivative and equal it to zero as the following :
p = 2x + (288/x)
p ' = 2 - (288/x^2)
0 = 2 - (288/x^2)
(288/x^2) = 2
(288/2) = x^2
144 = x^2
x = +/- 12 =====> ignore negative numbers in dimensions
x = 12 ft
A = x * y
144 = 12 * y
y = 12
it means it is a square with 12 * 12 = 144 ft^2
the least possible perimeter is :
p = 2 * x + 2 * y
p = 2 * 12 + 2 * 12 = 48 ft