ENG1090 Assignment 3: Foundation Mathematics Sem1, 2025 | Monash

ENG1090 Assignment Questions

Question 3.1 (7 marks)

Consider the function ƒ : [2,2] → R defined by f(x)=(3x2) · e ̄a·

1. Determine all of the critical numbers of f.
2. Use the second derivative test to classify all critical numbers of f.
3. Determine the global maximum and minimum of f.

Question 3.2 (4 marks)

The curves y = 0, y = √ and y = √2-enclose a region R in the Cartesian plane shown below.

1. Calculate the area A of R. 

Question 3.3(8 marks)

A rod of length3has a densityρ: [0,3]→Rsatisfying

Calculate the centre of mass¯xof the rod.

Question 3.4(12 marks)

The curve implicitly defined byy2= 4x2(1−x2 )is shown below.

The curve is symmetrical in both axes

1. Find an expression for dy when y+0.
2. Find the coordinates of all points on the curve where the tangent to the curve is parallel to the x-axis.
3. What is the area A of region enclosed by the curve?