you are given the graph of a function f. determine the intervals where the graph of f is concave upward and…

you are given the graph of a function f. determine the intervals where the graph of f is concave upward and where it is concave downward. (enter your answers using interval notation.) concave upward concave downward

you are given the graph of a function f. determine the intervals where the graph of f is concave upward and where it is concave downward. (enter your answers using interval notation.) concave upward concave downward

Answer

Explanation:

Step1: Recall concavity definition

A function is concave - upward when its second - derivative is positive and concave - downward when its second - derivative is negative. Visually, a function is concave upward if it "holds water" and concave downward if it "spills water".

Step2: Analyze the graph

Looking at the graph of the function (y = f(x)), we can see that the graph is concave upward on the intervals ((0,1)) and ((3,4)) because in these intervals, the graph has a shape that would hold water. The graph is concave downward on the interval ((1,3)) because in this interval, the graph has a shape that would spill water.

Answer:

concave upward: ((0,1)\cup(3,4)) concave downward: ((1,3))