Posted by Cecille on Tuesday, February 22, 2011 at 6:57pm.
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 commaseparated 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.)
I realy don't know how to do these problems.. please help

Calculus Please Help  MathMate, Tuesday, February 22, 2011 at 10:27pm
For a function to be increasing on ℝ and concave downwards, it must:
1. have no maximum/minimum, because it is a onetoone function.
2. Crosses the xaxis (or any other yvalue) at most once, since it is an increasing function.
3. Since it is concave down, d²y/dx² must be negative.
Study the above statements. If you do not know why they are true, refer to your notes, your textbook, or post.
I have taken an example function that satisfies these two properties is f(x)=3e^(x). (There may be many other functions that have these properties.) See the following link for its graph:
http://img268.imageshack.us/i/1298419029.png/
A. Since we know that f(13)>0, then the zero of the function, if any, must happen when x<13 for an increasing function. Beyond 13, x continues to increase, and therefore cannot have zeroes.
B. If f'(13)=1/4, and we know that f"(x) is negative throughout the domain of f(x), what can you say about f'(x) for x>13? Would it not be true that f'(x)<1/4 for x>13?
So what happens to to f'(x) <13?
C. The limit for the example function is 3, (but f(x) does not satisfy the required conditions of f(13)=3 and f'(13)=1/4.) Some parameters are required. It was just for illustration purposes.
Answer This Question
Related Questions
 Calculus Please Help  A continuous function f, defined for all x, has the ...
 calculus  You are given that f(x) =1+ax+ax2 f′(x) =−(x+2)ax3 f&#...
 Calculus  Let f be the function defined for x >or= to 0 with f(0)=5 and f', ...
 calculus  Consider the exponential function . Which of the following best ...
 Calculus  Suppose that f(x), f'(x), and f''(x) are continuous for all real ...
 Calculus  Sketch the graph of the function that has the following properties. f...
 calculus  Please help me solve. I think increase = concave up and decrease = ...
 Calculus  The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), ...
 calculus  Given f(x)=sin(x)2cos(x) on the interval [0,2pi]. a) Determine where...
 Calculus  If the functions f and g are defined for all real numbers and f is an...
More Related Questions