Graphical Second Derivative

2ndDerivative

Observe that the graph of $y=f(x)$ is concave up for $x<0$ , implying $f''(x)>0$ for $x<0$ . Similarly, the graph of $y=f(x)$ is concave down for $x>0$ , implying $f''(x)<0$ for $x > 0$ . Only graph B meets these conditions, implying B is the only possible graph of $f''(x)$ .

The graph y = f(x) shows negative y values for x < 0 and Positive y values for x > 0. Therefore the differentials will be respectively positive and negative y for the given ranges. Only graph C satisfies these conditions. Moreover, the first derivative of a curved function cannot be a straight line, making C and D impossible.