Math. 128 Sample test 3
1) Find dy/dx using implicit differentiation 2x3 - 3y2 = 4
2) Use differentials to approximate
a) (99.7)1/2
b) the change in value of function f(x) = 2x1/2 -3 as x
changes from 4 to 4.5.
c) ex. 34/769
choose one
3) Find interval(s) where f(x) = x3/3 - x2 + x - 3 is
increasing
4) Find horizontal and vertical asymptotes (if any) of
f(x) = (x2 + x)/[x(x - 1)].
5) Find absolute max. value of f(x) = x/(x2 + 1) on [0, 5].
6) Find relative max/min (if any) of f(x) = 3x4 - 2x3 + 4.
7) ex. 35/831
8) ex. 43/758, ex. 50/759, ex. 30/745 (choose one)
9) Solve for x, 12 - e0.4x = 3.
10) Find the equation of the t-line to the graph of f(x) =
e2x-3 at (2/3, 1).
11) Find derivative of f(x) = (ex + 1)/ex.
12) Find inflection point of f(x) = xe-2x.
13) Find second derivative of f(x) = 2(lnx)3/2.
14) Find the general antiderivative of (choose one)
a) f(x) = 3x - 1
b) f(x) = 7
c) evaluate dx
∫
Choose any 11 exercises. This sample test does not
represent the whole material included in sections 11.5 -
14.1. It is absolutely necessary to complete all exercises
listed in syllabus as homework.