Questions: Select the correct graph of the derivative of the function f(x) given below.

Solution Steps

The line passes through the points $(0, 3)$ and $(1.5, 0)$.

The slope of the line is given by $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{1.5 - 0} = \frac{-3}{1.5} = -2.$$

Since the graph of $f(x)$ is a straight line, its derivative is constant and equal to the slope of the line. Therefore, the derivative of $f(x)$ is $f'(x) = -2$. The graph of $f'(x)$ is a horizontal line at $y = -2$.

Final Answer