Practice Exam 2
the linear approximation to estimate .
are using Newton’s formula to estimate the root of x3 – 3x + 1. If x5 = 0.2, what is x6?
the absolute maximum and minimum value of the function f(x) = x 4
– 8x2 +1 on the interval [-1,3].
the function f(x) =
give the intervals where f is
increasing-decreasing, concave up-down, list the inflection points and local
maxima and minima (Use either the first or second derivative test to justify
Same thing for f(x) = x3 – 6x2
– 20x + 2.
farmer wishes to fence in a rectangular pasture with one side bounded by a
straight river bank. He wants to divide the pasture in half with a length
of fence running parallel to the river. If he has 2000 feet of fencing,
what is the maximum total area he can enclose.
Other sample problems : p. 306 –
a graph of f(x) = x/(x-1). Include the details listed by the text.
the antiderivatives: (a) 3x + 4, (b) 5sec 2x
(c) e-x + cos(x)
(d) x-1 + x-2
the Mean Value Theorem. Find the point c guaranteed by the Mean Value
Theorem for f(x) = 4x – 1/x on the interval [1,2]. What if the interval is
L’Hopital’s rule or some other rule to find the limits: