00:01
Here we are asked to find the graph of the derivative of the given graph.
00:06
It is easy to observe that the given graph is a parabola which is open upward and it passes through the origin 0 comma 0.
00:17
Now recall that the text form of a general parable arm can be given by y is equal to a times x minus h bfold square plus where the point h comma k indicates the vertex.
00:38
We know that vertex of the parabola is either the maximum point or the minimum point of the parabola.
00:51
In our case the minimum point is at the origin.
00:57
Why because that is where the function value becomes minimum.
01:01
So, the general equation of the given parabola becomes y is equal to a times x square.
01:13
As we know that, the value of h and k are zeros.
01:17
That is, the parabola in the question can be denoted like this.
01:23
Here understand that as our parabola in the question is open upward, the value of a in this equation will be positive.
01:36
Now we need to find the graph of derivative of this function.
01:41
Therefore differentiating y with respect to x will give as y -dash is equal to 2 times a x where a is greater than 0.
01:54
Here we can observe that the derivative of the function is linear...