Construct a graph from the following data and consider tangents drawn at x = 2, 4, 6 , and 8 . Identify the correct equation of the curve and the expression for the slope of the tangent ( = dy dx ) . x 1 2 3 4 5 6 7 8 9 10 y 2 8 18 32 50 72 98 128 162 200

Step-by-step solution

From the given table, the relationship between x and y can be observed as follows: For x = 1 , y = 2 = 2(1)^2 For x = 2 , y = 8 = 2(2)^2 For x = 3 , y = 18 = 2(3)^2 In general, the equation of the curve is y = 2x^2 . The slope of the tangent is given by the derivative of y with respect to x . dy dx = d dx (2x^2) = 4x