How to draw the graph if the derivative function is given in the question?

2 Answers

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to find the equation of the original function, hence you need to find the antiderivative of the function.

If the derivative of the function is f'(x) => you will find the antiderivative by integrating f'(x).

`int f'(x)dx = f(x).`

The graph of f(x) depends on the type of the function f(x).

If you know how the graph of the derivative looks like, then you may find the stationary points of the function the same place the graph of derivative intersects x axis (the roots of derivative are the extreme points of the function).

maccadee's profile pic

maccadee | Student, Undergraduate | (Level 1) eNoter

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when the graph of f'(x) is positive on a given interval, then the graph of f(x) is increasing. if f'(x) is negative, then f(x) is decreasing.

if the graph of f'(x) changes from positive to negative (or if f'(x) crosses the x-axis downward) then the graph of f(x) has a local maximum. if the graph changes from negative to positive (crosses x-axis upward) then the graph has a local minimum.

hope this helps :)