Question

(a) the open intervals on which f is increasing. (enter your answer using interval notation.)
(0,1)\cup(3,7)
(b) the open intervals on which f is decreasing. (enter your answer using interval notation.)
(1,3)
(c) the open intervals on which f is concave upward. (enter your answer using interval notation.)
(d) the open intervals on which f is concave downward. (enter your answer using interval notation.)
(e) the coordinates of the points of inflection.
(x,y)=( ) (smallest x - value)

Explanation:

Step1: Analyze concavity

Concave upward means the graph bends upwards like a cup. Concave downward means it bends downwards like a cap. A point of inflection is where the concavity changes.

Step2: Identify concave upward interval

Looking at the graph, the function is concave upward on the interval \((2,5)\).

Step3: Identify concave downward interval

The function is concave downward on the intervals \((0,2)\cup(5,7)\).

Step4: Find points of inflection

Points of inflection occur where concavity changes. At \(x = 2\) and \(x=5\). When \(x = 2\), \(y\) - value (from graph) is \(0\) and when \(x = 5\), \(y\) - value (from graph) is \(2\).

Answer:

(c) \((2,5)\)
(d) \((0,2)\cup(5,7)\)
(e) \((2,0)\) (smallest \(x\) - value) and \((5,2)\)