1. The problem is to understand what turning points are in the context of graphs, especially for IGCSE 10th grade. 2. A turning point on a graph is a point where the graph changes direction from increasing to decreasing or from decreasing to increasing. 3. Mathematically, turning points occur where the derivative of the function equals zero, i.e., where $f'(x) = 0$. 4. Important rule: At a turning point, the slope of the tangent to the curve is zero. 5. For example, consider the function $y = x^2$. 6. Its derivative is $y' = 2x$. 7. Set the derivative equal to zero to find turning points: $$2x = 0$$ 8. Solving gives $x = 0$. 9. Substitute back into the original function to find the turning point coordinates: $$y = (0)^2 = 0$$ 10. So, the turning point is at $(0,0)$. 11. This point is a minimum because the graph changes from decreasing to increasing. 12. In summary, turning points are where the graph changes direction, found by setting the derivative to zero and checking the nature of the point.