00:01
In subpart a of this problem, we are provided with the function p of x, which equals to f of x times g of x and we are asked to find out p prime of 8.
00:17
So first let us look at p prime of x.
00:20
P prime of x by the product rule equals to f of x times g prime of x plus f prime of x times g of x.
00:31
So now let us substitute the value of x as 8.
00:34
We have p prime of 8 to be equal to f of 8 times g prime of 8 plus f prime of 8 times g of 8.
00:46
So from the graph it is clear that the value of f of 8 is 6 and the value of g of 8 is 2.
00:54
Now let us calculate the values of f prime of 8 and g prime of 8.
00:58
So for this we make use of two points in the graph where f of 8 is present.
01:08
So this is because f prime of 8 is the slope at x equals to 8.
01:14
So we can find out the slope using the points 8 comma 6 and 7 comma 4.
01:22
So using these two points we have the difference of the y values that is 6 minus 6.
01:28
Minus 4 over the difference of the x values which is 8 minus 7 this equals to 2 over 1 which is 2.
01:36
So this is the value of f prime of 8.
01:38
Next we calculate g prime of 8 using the points 2 comma 8 and 3 .6.
01:44
So using these 2 we have sorry we calculate g prime of 8 using the points 8 comma 2 and 6 comma 3.
01:53
So using these 2 minus 3 that is the difference in the 5 values over 8 minus 6 the difference in the x values.
02:02
So this equals to negative 1 over 2.
02:05
So now that we have found the values, we substitute them.
02:08
We have p prime of 8 to be equal to f of 8 which is 6 times g prime of 8 which is negative 1 over 2 plus f prime of 8 which is 2 times g of 8 which is 2 as well...