Answer
See explanation
Work Step by Step
The slope of the secant line is:
$$\frac{f(2.5)-f(2)}{2.5-2}=\frac{2.5-2}{2.5-2}=1$$
The equation of the tangent line to the graph of $f$ at $x=2$ is:
$$y=f(2)+f'(2)(x-2)$$ where $f'(2)$ is the slope of the line.
Since the red line is the tangent line to the graph of $f$ at $x=2$ it follows that $f'(2)$ is its slope.
Notice as the tilt of the line is large as the slope is larger too.
The slope of the secant line is greater than the slope $f'(2)$ of the tangent line (red line) to $f$ because the tilt of the secant line is greater than the tilt of the red line.
