University of Toronto Scarborough
MATA31 Assignment 8-Winter 2022
Read sections 2.1-2.2
Solve the following problems. They are all important but just hand in
those that are in red color Your TA will mark the assignment and return it
to you the week after. In addition to accuracy, your solution must include
details and explanations to not lose any marks. This assignment is due to
Friday March 18, 5pm. It is worth 3%.
2.1: 22, 24, 26, 28, 30, 58
2.2: 10, 12, 18, 24, 26, 28, 30, 40, 42, 44, 46, 54, 56, 58, 60, 62, 70, 72, 74,
76, 78, 80, 92
A. Find numbers A and B such that derivative of the following function
is every where continuous
f(x) =

Ax3 + Bx + 2, if x ≤ 2
Bx2 − A, if x > 2
Hint: First of all, this function needs to be continuous.
B. Prove that the derivative of an odd function is an even function.
C. The greatest integer function is defined by
f(x) = [[x]] = the largest integer that is less than or equal to x
For example [[4]] = 4, [[2.8]] = 2, [[−1]] = −1, [[−3.5]] = −4. Sketch the curve
of f . At which points the function is not differentiable? Find a formula for
f ′ and sketch the curve of f ′ for those values that function is differentiable.