1. The problem is to identify which graphs represent the gradient (derivative) functions of given graphs A, B, and D, and to find one other pair of graphs where one is the gradient function of the other. 2. Recall that the gradient function of a curve shows the slope of the tangent line at each point on the original curve. 3. For graph A, which is a cubic-like curve with one local maximum and one local minimum crossing the x-axis thrice, its gradient function should be a quadratic curve with two roots (where the slope is zero) corresponding to the local max and min of A. Among the graphs, C and D are parabolas. Since A has a local max and min, its gradient is a parabola opening downward or upward. Graph C is a downward-opening parabola peaking above the x-axis, and D is an upward-opening parabola with vertex below the x-axis. The gradient of a cubic with one max and one min is a quadratic with two roots, so graph C fits as the gradient of A. 4. For graph B, another cubic-like curve with one local minimum and one local maximum, its gradient function is also a quadratic with two roots. Graph D is an upward-opening parabola with vertex below the x-axis, which fits the gradient of B. 5. For graph D, an upward-opening parabola with vertex below the x-axis, its gradient function is a straight line with positive slope (since derivative of a quadratic is linear). Graph H is a straight line passing through the origin with positive slope, so H is the gradient function of D. 6. The problem states there is one other graph which is the gradient function of another graph shown. Graph F is a straight line with negative slope crossing the y-axis above zero, and graph G is a horizontal line below the x-axis. The derivative of a linear function is a constant (horizontal line). So G is the gradient function of F. Final answers: - Gradient of A is graph C. - Gradient of B is graph D. - Gradient of D is graph H. - Gradient of F is graph G.