1. The problem states that the derivative of the function $f$ at $x = -8.9$ is $f'(-8.9) = 4.53073$. 2. This means the slope of the tangent line to the curve of $f$ at the point where $x = -8.9$ is approximately $4.53073$. 3. The derivative $f'(x)$ gives the instantaneous rate of change of the function $f$ at any point $x$. 4. Since $f'(-8.9) > 0$, the function $f$ is increasing at $x = -8.9$. 5. The tangent line at $x = -8.9$ can be expressed as: $$y = f(-8.9) + f'(-8.9)(x + 8.9)$$ where $f(-8.9)$ is the function value at $x = -8.9$. 6. Without the exact value of $f(-8.9)$, we cannot write the full equation of the tangent line, but we know its slope is $4.53073$. 7. This slope indicates how steep the curve is at that point, and the positive value means the curve is going upwards as $x$ increases past $-8.9$. Final answer: The slope of the tangent line to $f$ at $x = -8.9$ is $4.53073$, indicating the function is increasing there.