# Derivative and continuous function graph

• Oct 11th 2012, 11:59 AM
Kathrynm77
Derivative and continuous function graph
f(x)= {2x-x^2. For x is less than or equal to 1
{x^2 -2x +2. For x >1

a)for what values of k and p will f be continuous and differentials at x=1?
b) for the values of k and p found in part a on what intervals in f' positive
C)give a graphical interpretation for the graph of f for those values of x for which f' is popositives
i got k to equal -2 and p to equal 2
but I don't know how to tell if its positive...isn't just where it's above the x axis?...so then the graph of f' would look like an absolute value function with vertex at 1 and the graph where f' is positive would be the same graph because it does not cross the x axis into the third and forth quad
• Oct 11th 2012, 12:10 PM
HallsofIvy
Re: Derivative and continuous function graph
Quote:

Originally Posted by Kathrynm77
f(x)= {2x-x^2. For x is less than or equal to 1
{x^2 -2x +2. For x >1

a)for what values of k and p will f be continuous and differentials at x=1?

??? There is no k or p in the problem. Have you already replaced them with "-2" and "2"?

Quote:

b) for the values of k and p found in part a on what intervals in f' positive
C)give a graphical interpretation for the graph of f for those values of x for which f' is popositives
i got k to equal -2 and p to equal 2
but I don't know how to tell if its positive...isn't just where it's above the x axis?...so then the graph of f' would look like an absolute value function with vertex at 1 and the graph where f' is positive would be the same graph because it does not cross the x axis into the third and forth quad
What is the derivative of f? You seem to be confusing f'(x) with the graph of f(x). To say that f is positive on an interval means that it take on only positive values in that interval. Which is the same as saying its graph is above the x-axis. But be careful, 0 is NOT positive.
• Oct 11th 2012, 12:30 PM
Kathrynm77
Re: Derivative and continuous function graph
Sorry I totally goofed yes k and p were replaced when I typed that