Mathematics Assignment | New

Running head: MATHS ASSIGNMENT
MATHS ASSIGNMENT
Name of the Student
Name of the University
Author Note

MATHS ASSIGNMENT1
1.
a) y = x^4 – 36x^2
x-intercept => 0 = x^4 – 36x^2
 x = 0, 6,-6
hence, x intercepts are (0,0), (6,0), (-6,0)
y intercept => y = 0
 (0,0)
Stationary points => dy/dx = 0
 4x^3 – 72x = 0
 (x^2 – 18)x = 0
 x = 0 and x = ±√18 = ±4.242
Hence, points are (0,0), (-4.242,-324), (4.242,324)
Points of inflection => ( d
dx )( dy
dx )=0
 12x^2 – 72 = 0
 x^2 – 6 = 0
 x = ± √ 6 = ±2.449
Hence, points are (-2.449,-179.942) , (2.449,-179.942)
Graph of curve with all points:

MATHS ASSIGNMENT2
b)
From the curve it can be seen that the function is non-negative in the interval (-∞,-6] U [6,∞).
The function is increasing in the interval (-4.243,0) U (4.243,∞).
The function is concave up in the interval (-6,0) U (0,6).
2.
a) Given, the area of rectangular garden is 400 m^2.
Given, length of one side of garden = x meters.
Hence, length of other side of garden = 400/x meters.