1. Use an appropriate tangent line approximation to estimate (8.1)1
3
2. The length of a side of a cube is measured to be 10 cm with a possible error of + −.1 cm.
What is the maximum possible error if this measurement is used to determine the volume of
the cube?
3. Sketch the graph of a function y=f(x) such that
(a) f(x)≥0 for all x.
(b) f(0) = 0.
(c) lim
x→∞
f(x) = 0
(d) f0(x)<0 when 1 ≤x≤3.
(e) f00(x)>0 when 2 <x<4
4. The graph of y=f(x) is given below.
(I.)
(a) When is f0(x)>0?
(b) When is f00(x)<0?
(c) What are the critical points of f?
(d) What are the inflection points of f?
5. Find the absolute maximum and minimum of x3−6x2+ 9x+ 3 on the interval [0,4].
6. For each of the following functions find the critical numbers and determine whether each is a
local max, a local min, or neither.
(a) 3x4−4x3+ 7
(b) x1
3(x−1)2
3
7. Suppose that
f(x) = x2+ax +b
for some constants aand b. If x= 1 is a critical number of fand f(1) = 6 what are aand b?
8. Let f(x) = x3−x2+x+ 4. Find the cwhich satisfies the mean value theorem applied to f
on the interval [1,2].
9. Is there a differentiable function such that f(0) = 0, f(1) = 7, and f0(x)≤5? If so then find
one, if not they explain why not.
