Weekly Tutorial 3 for Math. 69.007A,
Introductory Calculus I

Instructor: Dr. Angelo Mingarelli

Notes: These are group tutorials; each question is to be divided among the group (at most 5 students in a given group), solved and submitted to the T.A. at the end of the 50 min. period. NOTES PERMITTED, along with group interaction...All students within a group will be assigned the same grade for this tutorial...
This online test is meant to be printed and handed in.
Solutions will appear later on during the term ...

Group names (Please PRINT) & Student Numbers:

1. Calculate the derivative of the following function: f(y) = sqrt(y)[y - 2sqrt(y) + 2] at y = 4.
[Here, "sqrt" means the "square root of ..."]

a) 1/2
b) 3/2
c) 0
d) -1/2

2. Find the point on the curve y = x sqrt(x) where the tangent line is parallel to the line 6x - y = 4.
Don't forget that two lines are parallel if they have the same slope...

a) 4
b) 9
c) -4
d) 16

3.If h(t) = t2 + 6 and k(x) = x+ 2 what is the value of the composition (h o k)(2)?

a) 4
b) 22
c) 6
d) 10

4. Determine whether or not the function f(x) = x |x| is differentiable at x = 0.

a) No, because the left- and right-derivatives are unequal at x = 0,
b) Yes, because this function is actually equal to x2 for any value of x,
c) Yes, because the left- and right-derivatives are equal at x = 0,
d) No, because there is an absolute value multiplying the "x"

Solutions are given within the box:

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