The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)g(x). Find each of the following:
The graph:
Find each of the following what? You already showed the graph, so you should be able to figure out and as piecewise continuous functions.
Find the five slopes and five corresponding y-intercepts (to find the y-intercepts, you pretend that each line segment continues to figure out where it would hit the y-axis if it were a line). To be the most accurate, try to find specific points that the line segments cross. For example, the left-most red line segment passes between the points and , so you can use those points to find the slope of that line segment, which would tell you .
What else do you need help figuring out?
The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)g(x). Find each of the following:
u(1) =
v(1) =
this is the actual question
so to find u'(1), I would need to use the product rule?
If I read it correctly (and there are some strange characters in the post), u= f times g and v= f divided by g.
Yes, by the product rule, u'= f'g+ fg' and by the quotient rule, v'= (f'g- fg')/v^2. Now, from the graph, f' is -3 for x< 0, 2 for 0< x< 3, and -1 for x> 3 while g' is -3/2 for x< 2 and 1/2 for x> 2.