Question

How to draw the derivative on the graph?

Answer 1

The value for `x` for which `y=f(x)` has a stationary point is the value of `x` at which `f'(x) = 0`.

Explanation:

The tangent at a point on the Graph of `f(x)` gives the value of Derivative at that point.

But here directly the graph of `f'(x)` is given and not of `f(x)` which makes this problem simpler.

So here in first graph the stationary points are `-1, 1 , 5`

and in the second graph the stationary points are `0` and `2`.

For first graph :

`x=-1` is the Point of Inflection ,
`x=1` is a point of Local minima
and `x=5` is a point of Local maxima.

For second graph :

`x=0` is a point of Local maxima
and `x=2` is a point of Local minima.

For your reference see this pic given below :-