The curve f(x) = x^2 plus 2x is taken at the point where x = 1. What is the equation of the tangent to the curve there?

1. A tangent needs two things, a point it passes through and its gradient. 2. Find the point first by substituting x equal to 1 into the function. 3. One squared is 1 and 2 multiplied by 1 is 2, so the point is 1 comma 3. 4. Now find the gradient. The derivative of x squared plus 2x is 2x plus 2. 5. Substituting x equal to 1 gives 2 plus 2, so the gradient of the tangent is 4. 6. Use the gradient point form, so y minus 3 equals 4 multiplied by x minus 1. 7. Expanding gives y minus 3 equals 4x minus 4, so y equals 4x minus 1. 8. The line y = 4x + 3 is the trap for using the y value as the intercept without shifting it, y = 3x - 1 uses the y coordinate as the gradient, and y = 2x + 1 stops at the coefficient of x in the derivative. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_