9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down,...
Find where the graph of f is increasing, decreasing, concave upward and concave downward then find any intercepts, relative extrema, points of inflection, and asymptote. Use this information to sketch the graph of f.f(x) = (2x-1)2(x-3) (x-7)
4. For the following function f find the domain; the asymptotes ;intervals where f is increasing, decreasing, concave upward, concave downward; local maximum, minimum and inflection points; sketch the graph: f(x) = 1/(x-1)3
2. f(x) = x? – 3x² +5. a) (5 pts) Find the (x, y) coordinates of the critical points. b) (5 pts) Find the (x, y) coordinates of the point of inflection (point of diminishing return) c) (5 pts) Over what interval is the function increasing/decreasing and over what interval is the function concave up/concave down? Analytically test for concavity. d) (5 pts) Use the 2nd derivative test to determine (x, y) coordinates of the relative max/min.
Graph the polynomial using calculus methods. F(x)= 7/3 x3 + 13/2 x2 -12x +3 List local extrema, intervals of concavity, and inflection point(s) if they exist. Local maximum: Local Minimum: Concave up: Concave down: Inflection point(s):
2. for the function f(x)= x+2 cos x on the interval
[0,2pi] a. find the first derivative
b.) find the second derivative
c.) find the functions critical values(if any). include their y-
coordinates in your answers in order to form critical points.
d. )find the intervals on which f is increasing or
decreasing.
e. )find the local extrema of f.
f. )find the functions hyper critical values(if any). include their
y coordinates
g.) find the intervals of concavity, i.e. the...
2. Determine where the functions below are increasing and decreasing, and where in the graphs they are concave up and concave down. Find the relative extrema and inflection points. a. g(x)=V?+1 b. f(x)=
Determine the intervals on which f is increasing or decreasing, assuming the figure below is the graph of the derivative of f. On Interval 1: is ? < On Interval 2: f is? On Interval 3: fis ? 241 24.1 1 & -2411 If the figure below is the graph of the derivative f', answer the following: Where do the points of inflection of f occur? On which interval(s) is f concave down? 4,
Problem 5. (15 pts) Consider f(x) = -1x + +8. (a) Find and classify all local extrema. Where is S(x) increasing? Decreasing? Justify your answer. (6) Find all inflection points. Where is f(x) concave up? Concave down? Justify your answer. (c) From the information above, sketch f(a).
Sketch the graph of f(x)= (x^2)/(x^2-1), stating all relative extreme points, intervals of increasing and decreasing, intervals of concave up and concave down, inflection points, and asymptotes.
Determine the intervals on which the given function is concave up or down and find the point of inflection. Let f(x) = x(x - 5) The x-coordinate of the point of inflection is 225/64 , and on this interval f is The interval on the left of the inflection point is Concave Down The interval on the right is Concave Up and on this interval f is Determine the intervals on which the given function is concave up or down...