Find the point (x, y) on the Euclidean plane where the curve y = 2x2 - 2x + 3 has 2 as gradient
Answer Details
We know that the gradient of a curve is given by its derivative. Therefore, we need to find the derivative of the given curve and equate it to 2 to find the point where the gradient is 2. y = 2x^2 - 2x + 3 dy/dx = 4x - 2 Equating dy/dx to 2, we get: 4x - 2 = 2 4x = 4 x = 1 Substituting x = 1 in the original equation, we get: y = 2(1)^2 - 2(1) + 3 y = 3 Therefore, the point where the curve has a gradient of 2 is (1, 3). So, the correct option is: (1, 3).