A continuous function f, defined for all x, has the following properties:

1. f is increasing
2. f is concave down
3. f(13)=3
4. f'(13)=1/4

Sketch a possible graph for f, and use it to answer the following questions about f.

A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in an interval, the minimum and maximum are both N.)

−INF <x<= 0
0 <x<=1
1<x<13
13<=x<INF
I need the maximum and minimum... I just have the two first ones... 0 for both 1 and 2 maximum and minimum... then I really don't know what to do..

B. Are any of the following possible values for f'(1)? (Enter your answer as a comma-separated list, or enter 'none' if none of them are possible.) −3, −2, −1, −51, 0, 51, 1, 2, 3.
possible values: f'(1)=_________

C. What happens to f as x−>- INF?
lim x−> INF f(x)= ________

(Enter the value, 'infinity' or '-infinity' for or −, or 'none' if there is no limit.)

1. 👍 0
2. 👎 0
3. 👁 501
1. http://www.jiskha.com/display.cgi?id=1298419029

1. 👍 0
2. 👎 0

Similar Questions

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For

2. calculus

2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] . a. Find the absolute maximum and minimum values of f(x) b. Find the intervals on which f is increasing. c. Find the x-coordinate of each point of

3. calculus

1. Let f be the function that is defined for all real numbers x and that has the following properties. (i) f''(x)=24x-18 (ii) f'(1)=-6 (iii) f'(2)=0 a. Find each x such that the line tangent to the graph of f at (x, f (x)) is

4. calculus

if f is a continuous function defined by f(x)={x^2+bx, 5 sin("pie"/2x) then b= ?

1. Calculus

If f(x) is a continuous function defined for all real numbers, f(-1)=1, f(-5)=-10, and f(x)=0 for one and only one value of x, then which of the following could be that x value? a) -6 b) -5 c) -4 d) 0

2. Calculus (Continuity)

If the following function is continuous, what is the value of a + b? f(x) = {3x^2 - 2x +1, if x < 0 a cos(x) + b, if 0

3. math

Use a graph to determine whether the given function is continuous on its domain. HINT [See Example 1.] f(x) = x + 7 if x < 0 2x − 5 if x ≥ 0 1 continuous discontinuous If it is not continuous on its domain, list the points of

4. Calculus

Let f be the function defined by f(x)=xe^(1-x) for all real numbers x.: a. Find each interval on which f is increasing. b. Find the x-coordinate of each point of inflection of the graph of f

1. Calculus

Suppose that f(x), f'(x), and f''(x) are continuous for all real numbers x, and the f has the following properties. I. f is negative on (-inf, 6) and positive on (6,inf). II. f is increasing on (-inf, 8) and positive on 8, inf).

2. calculus

Let f be the function defined by f(x)= sqrt(x), 0

3. Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and

4. AP Calculous

let f be the function defined by f(x)=3X^5 -5X^3 +2 a) on what interval is f increasing? b) on what interval is the graph of f concave upward? c)Write the equation of each horizontal line tangent to the graph of f