Final answer:
To find the equation of the tangent line to the curve, we can take the derivative of the function y = (1 + 2x)¹⁰ to find the slope at the given point (0, 1). Using the slope and the point, we can then write the equation of the tangent line.
Step-by-step explanation:
To find the equation of the tangent line to the curve, we need to find the slope of the curve at the given point. We can do this by taking the derivative of the function y = (1 + 2x)¹⁰. The derivative of this function is 10(2x)(1 + 2x)⁹. Evaluating this derivative at x = 0 gives us the slope of the tangent line at the point (0, 1).
Substituting the values of x and y into the equation y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the tangent line, we can find the equation.
Plugging in the values x = 0, y = 1, and m = 20 into the equation, we get y - 1 = 20(x - 0), which simplifies to y = 20x + 1.