2. Now, Let's determine which is which...
-A derivative function is always above the x-axis
(positive) when the slope of the parent function
is positive, and negative when the slope is
negative. If this is the case, then then the only
pairs that fit this description are: B =f'(x) of D or
A=f'(x) of B.
-The second derivative of a function is always
positive when the parent function is concave up,
and negative when concave down. Based on this,
the only function that could be a second
derivative is A as that of D.
-Considering the second derivative is the
derivative of the first derivative:
A = f'(x) of B B=f'(x) of D
and
A f''(x) D
then
D=f(x)
B=f'(x)
A=f''(x)
3. Lets Have a look at these functions:
We notice that...
-At graph A's roots, graph D also has roots; at
these points, graphs C and B have local extrema
-When graph B has roots, so does graph C; also,
graph D has local extrema here.
-When graph B's slope is negative, graph A is
always positive. When it's positive, do is graph A
-When graph D's slope is negative, graph B is
always positive. When it's positive, so is graph B
-When graph D is concave up, Graph A is always
positive. When it's concave down, Graph A is
negative.
