Answer
Call the curve with the positive y-intercept g and the other curve h. Notice that g has a maximum (horizontal tangent) at
x = 0, but h $\ne$ 0, so h cannot be the derivative of g. Also notice that where g is positive, h is increasing. Thus, h = f and
g = f'
Now f'(−1) is negative since f' is below the x-axis there and f''(1) is positive since f is concave upward at x = 1.
Therefore, f''(1) is greater than f'(−1)
Work Step by Step
Call the curve with the positive y-intercept g and the other curve h. Notice that g has a maximum (horizontal tangent) at
x = 0, but h $\ne$ 0, so h cannot be the derivative of g. Also notice that where g is positive, h is increasing. Thus, h = f and
g = f'
Now f'(−1) is negative since f' is below the x-axis there and f''(1) is positive since f is concave upward at x = 1.
Therefore, f''(1) is greater than f'(−1)
