1 answer

How to draw the derivative on the graph?

Question:

enter image source here


Answers

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 :-

http://mathworld.wolfram.com/StationaryPoint.html

.

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