Find the equation of the tangent to y = 2x^2 + 7 at x = 3.

The first step here is to identify what to do. Differentiating the equation y = 2x^2 + 7 will result in dy/dx = 4x. Given that you know that x = 3, you can substitute x = 3 into 4x which gives you 4(3) = 12. Thus, you now know that the gradient is equal to 12 at the point x = 3. However, you are trying to find the equation of the tangent and so you use the equation y = mx + c to calculate the equation. You know that the values are m = 12, x = 3 but y and c are currently unknown. To find the value of y, you substitute x = 3 into the original equation of y = 2x^2 + 7 which gives you y = 25. Plug in the values into y = mx + c to find c and rearrange to find c. c = 25 - 36 = -11. Finally, putting all of these values together results in y = 12x - 11.