5. Consider the function f(x) = -x^3 + 2x^2 + 2.
(a) Find the domain of the function and all its x and y
intercepts.
(b) Is the function even or odd or neither?
(c) Find the critical points, all local extreme values of f, and
the intervals on which f is increasing or decreasing.
(d) Find the intervals where f is concave up or concave down and
all inflection points.
(e) Use the information you have found to sketch...
The function f(x, y) = 10−x 2−4y 2+2x has one critical point.
Find that critical point and show that it is not a saddle point.
Indicate whether this critical point is a maximum or a minimum, and
find that maximum or minimum value.
Consider the root of function f(x) = x 3 − 2x − 5.
The function can be rearranged in the form x = g(x) in the
following three ways: (a) x = g(x) = x3 − x − 5 (b) x =
g(x) = (x 3 − 5)/2 (c) x = g(x) = thirdroot(2x + 5) For each form,
apply fixed-point method with an initial guess x0 = 0.5 to
approximate the root. Use the error tolerance = 10-5 to...
(1 point) Suppose that f(x)=(12−2x)e^x.
(A) List all the critical values of f(x). Note: If there are no
critical values, enter 'NONE'.
(B) Use interval notation to indicate where f(x) is increasing.
Note: Use 'INF' for ∞, '-INF' for −∞, and use 'U' for the union
symbol. Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) List the x values of all local maxima of f(x). If there are
no local maxima, enter 'NONE'. x values...
In the function f(x) = 5x4-2x2-27 find the following:
a) their critical values
b)local maximum and minimum points
c)The intervals where the concavity is up and down
d) draw the graph and mark on it all the important points;
maximum, minimum and inflection points
Analyze the function given by f(x) = (2x − x^2 )e^x . That is:
find all x- and y-intercepts; find and classify all critical
points; find all inflection points; determine the concavity; find
any horizontal or vertical asymptotes. Finally, use this
information to graph the function.
1. Find the critical numbers for the following functions
(a) f(x) = 2x 3 − 6x
(b) f(x) = − cos(x) − 1 2 x, [0, 2π]
2. Use the first derivative test to determine any relative
extrema for the given function
f(x) = 2x 3 − 24x + 7