The average value of a function f over the interval [-2,3] is
-6, and the average value of f over the interval [3,5] is 20. What
is the average value of f over the interval [-2,5]?
Find the maximum rate of change of f at the given point
and the direction in which it occurs.
f(p, q) = 3qe-p +
2pe-q, (0, 0)
direction of maximum rate of change (in unit vector)
Determine whether Rolle's Theorem applies to the following
function on the given interval. If so, find the point(s) that are
guaranteed to exist by Rolle's Theorem. g(x)=x^3- 9 x^2 + 24 x -
20; [2,5]
A)Rolle's Theorem applies and the point(s) guaranteed to exist
is/arex=
(Type an exact answer, using radicals as needed. Use a comma
to separate answers as needed.)
B)Rolle's Theorem does not apply.
9. Given the function: f(x)=3x2+5x-17
a. find the interval where the function is increasing and where
it is decreasing.
b. Clearly state the critical number(s) of the function.
c. Find the relative extrema of the function( using 1st
derivative test). answer should be in (x,y)
10. Given the function: x3 - x2 + 52x -
17
a. determine the intervals where the graph of the given function
is concave upward and where it is concave downward.
b. Find any inflection...
given the function y=x+cosx on the interval [0,2pi] find the
intervals of increasing and decreasing, local or absolute
extrema(s), the intervals of concavity and the inflection points.
use the information to sketch the graph of y=x+cosx on the interval
[0,2pi]