Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn s y = 2x2 and the slope of tangent is tanθ = dy/dx= 4x. X 1 2 3 4 5 6 7 8 9 10 Y 2 8 18 32 50 72 98 128 162 200

Sol. The graph y = 2x2 should be drawn by the student on a graph paper for exact results. To find slope at any point, draw a tangent at the point and extend the line to meet x-axis. Then find tan θ as shown in the figure. It can be checked that, Slope = tan θ = dy/dx = d/dx (2x2) = 4x Where x = the x-coordinate of the point where the slope is to be measured.