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

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.

Re: Derivative and continuous function graph

Sorry I totally goofed yes k and p were replaced when I typed that