Final answer:
To find the equation for the tangent to the curve at the given point (2, 6), we find the derivative of the curve function and substitute the coordinates of the given point and the slope into the point-slope form of a line.
Step-by-step explanation:
To find the equation for the tangent to the curve at the given point, we need to find the derivative of the curve function. The derivative of y = x² + 2 is given by dy/dx = 2x. Next, we substitute the x-coordinate of the given point into the derivative to find the slope of the tangent line: m = 2(2) = 4. Finally, using the point-slope form of a line, y - y1 = m(x - x1), we substitute the coordinates of the given point and the slope to find the equation of the tangent line:
y - 6 = 4(x - 2)