How to draw the derivative on the graph?

Question

1594 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-21T00:48:56

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

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 :-

![http://mathworld.wolfram.com/StationaryPoint.html]( useruploads.socratic.org )