00:01
In this problem we are provided with the following graph and we are asked to find out the graph of the first derivative of this function.
00:14
So here let us analyze this graph.
00:18
In this graph it can be seen that the function is increasing from negative infinity up to negative 5 since as the values of x gone increasing, the values of y are also increasing.
00:33
Next, from negative 5 up to 0, it can be seen that the graph is decreasing as the values of x go on increasing, but the corresponding values of y are decreasing.
00:47
Next, from 0 up to 5, the values of x are increasing and the values of y are also increasing.
00:58
But from 5 up to infinity as the values of x go on increasing the corresponding values of y are decreasing so now let us write this down we have the intervals negative infinity negative 5 negative 5 0 0 5 5 and 5 up to infinity we know that when a function is increasing the first derivative of the function of the function is greater than 0 and when the function is decreasing the first derivative of the function is less than 0 so now here we have in the first interval the function is increasing so the value of the first derivative would be greater than 0 in the second interval the function is decreasing so the value of the function would be less than 0 in the third interval again the value of the function is increasing so the first derivative is greater than 0 and from 5 up to infinity the function is decreasing.
02:05
So the first derivative is less than 0.
02:08
So now let us make use of this information.
02:12
We first consider the coordinate plane from negative infinity up to negative 5...