calc

[lulln]

Hi,
I would like to know how to solve the graph- sketch a function f(x) with the following properties
f'(x) < 0 and f''(x)=0, for x< 2
f'(x) > 0 and f''(x)=0, for x >2
I have an idea, maybe the concave is going down, but not sure how to start. Thank you in advance!

 

[pka]

I would like to know how to solve the graph- sketch a function f(x) with the following properties
f'(x) < 0 and f''(x)=0, for x< 2
f'(x) > 0 and f''(x)=0, for x >2
I have an idea, maybe the concave is going down, but not sure how to start. Thank you in advance!

Here is the graph. May I suggest you consider \(f(x)=\sqrt{(x-2)^2}\).

 

[lulln]

Here is the graph. May I suggest you consider \(f(x)=\sqrt{(x-2)^2}\).

thanks.

 

[Dr.Peterson]

Hi,
I would like to know how to solve the graph- sketch a function f(x) with the following properties
f'(x) < 0 and f''(x)=0, for x< 2
f'(x) > 0 and f''(x)=0, for x >2
I have an idea, maybe the concave is going down, but not sure how to start. Thank you in advance!

Do you recognize that if f'(x) < 0, then the slope is negative so the graph is going down? And if f''(x)=0, what does that tell you? Concave down would mean f''(x)<0, wouldn't it? Rather, if the second derivative is 0, what must be true of the first derivative?

Use that kind of thinking to sketch a possible function, in two parts (left and right of 2).

You don't need to write out the function; problems like this commonly don't have a single answer, and sometimes it would be very hard to write the function anyway. All it says is to "sketch" (not write an equation for) the graph of "a function" (not "the" function).

In particular, contrary to pka's use of the word "the", there is not just one answer to this one. (All possible answers are closely related, though.)

Try making a graph different from his that fits the requirement. This is a valuable thing to do.