# Thread: behavior of a function

1. ## behavior of a function

Let F(x) be antiderivative of f(x)
(1) where is F(x) increasing and decreasing explain why?
(2)where is F(x) concave up and concave down explain.
(3)where does F(x) has inflection point
(4) where F(x) has maxima and minima.
(5)Using your answer to these question make a rough sketch of antiderivative F(x) on same set of axis as f(x), given that F(0)=0
On your sketch label where F(x) is maxima , minima and inflection point,concave up and down, increasing and decreasing.

2. Originally Posted by bobby77
Let F(x) be antiderivative of f(x)
(1) where is F(x) increasing and decreasing explain why?
It is where the original function (its derivative) is positive and negative.
Thus, it decreases on $\displaystyle x<0,x>2$
It increases on $\displaystyle 0<x<2$
(2)where is F(x) concave up and concave down explain.
It is where the derivative of this is increasing and decreasing. Quite difficult to tell from your picture.
(3)where does F(x) has inflection point
Where derivative is zero, at the max and min points of this graph.
(4) where F(x) has maxima and minima.
Where derivative is zero, i.e. where it crosses the x-axis. Those are your critical points.