Question

lesson 18: more on polynomial functions and modeling
score: 67.74/100 answered: 12/15
question 13
which description best matches the shape of the graph?
decreasing & concave up
decreasing & concave down
increasing & concave down
increasing & concave up

Explanation:

Step1: Analyze the increasing/decreasing nature

As \(x\) increases (from left - to - right on the graph), the \(y\) - values of the function are getting larger. So, the function is increasing.

Step2: Analyze the concavity

The second - derivative test for concavity: A function \(y = f(x)\) is concave up if \(f''(x)>0\) and concave down if \(f''(x)<0\). Geometrically, a concave - up function "holds water" and a concave - down function "spills water". For the given graph, if we consider two tangent lines at two different points \(x_1

Answer:

Increasing & Concave Up