1. **State the problem:** We need to estimate the gradient (slope) of the curve $y=f(x)$ at the point where $x=3$. 2. **Understanding the gradient:** The gradient at a point on a curve is the slope of the tangent line at that point. Since we only have a graph, we estimate the gradient by finding the slope of the secant line between two points close to $x=3$. 3. **Choose points near $x=3$:** From the description, the curve dips below $y=0$ near $x=2$ and rises sharply past $y=4$ near $x=5$. We pick points at $x=2.5$ and $x=3.5$ to estimate the slope at $x=3$. 4. **Estimate $y$ values:** - At $x=2.5$, the curve is slightly below $0$, estimate $f(2.5) \approx -0.5$. - At $x=3.5$, the curve is rising, estimate $f(3.5) \approx 2.5$. 5. **Calculate the gradient:** $$ \text{slope} = \frac{f(3.5) - f(2.5)}{3.5 - 2.5} = \frac{2.5 - (-0.5)}{1} = \frac{2.5 + 0.5}{1} = \frac{3}{1} = 3 $$ 6. **Interpretation:** The estimated gradient of the curve at $x=3$ is approximately $3$. This means the curve is rising steeply at that point. **Final answer:** The estimated gradient at $x=3$ is $3$.