Question

assignment 4 online mth 141 - 010 due: thursday, october 9, 2025 points: 20 points 1. (1 point) for the function f, whose graph is shown below, determine the sign of each of the following: positive, negative, or zero. a. f(0): ______ b. f(4): ______

Explanation:

Step1: Recall second - derivative property

The second - derivative $f''(x)$ determines the concavity of the function. If the function is concave up at a point $x$, then $f''(x)>0$. If it is concave down, then $f''(x)<0$.

Step2: Analyze concavity at $x = 0$

Looking at the graph near $x = 0$, the function is concave down. So, $f''(0)<0$.

Step3: Analyze concavity at $x = 4$

Looking at the graph near $x = 4$, the function is concave up. So, $f''(4)>0$.

Answer:

a. negative
b. positive