00:01
In this problem we have to use the graph of f and g.
00:05
So this is the graph for f and this one is graph for g.
00:11
Now we have given here px and qx.
00:15
So px is given fx into gx and p -dash and qx is given as p -x is equal fx y gx.
00:36
Xx now we have to find here p -dase 5 and q -dice 4 to find p -dase 5 and q -d -f so to find p -d -5 and q -d -s so to find this we will take derivative of the function px so p -d -x equal d by d x and fx into g x so using product rule of differentiation it can be written as f x into g -dase x and plus f -dash -x into g x so this is p -dase x now at x equal 5 so p -dash 5 equal f5 into g -dash 5 and plus f -d -d -5 into g -5 now using this graph, this is the graph g and this is the graph f.
01:49
So f5 is, so f5, this point is f5 is 6.
01:56
We have f5 is 6 and g dash 5 at the point x equal 5, the function gx is a horizontal function.
02:08
So the derivative of this function at any point between this 3 to 6 will be 0.
02:17
So g -dice 5 equal 0.
02:21
Or in other terms, we can say that the slope of this line at the given point is 0.
02:28
So g -d -5 equal 0.
02:31
So we will put 0.
02:33
Now to find f -d -5, so this is line and point.
02:39
5 is here to find the slope so f dash 5 is the slope of this given line at the point x equal 5 so this point is let's take this point is 3 .8 and this point is 7 .4 so f dash 5 will become slope up the line passing between these two lines so f dash 5 will become 4 minus 8 by 7 minus 3 that is minus 4 by 4 this is equal to minus 1.
03:22
F dash 5 is minus 1 and g 5 is 0 .g 5 is 0 .5 is 0 .5 and function g is so this is equal to 3.
03:36
So we have p dash 5 equal minus 3...