Question

Find the equation of the tangent line to the curve y = x^2 + 1 at the point (1, 2).

A. y = 2x + 1
B. y = 2x - 1
C. y = x + 1
D. y = x - 1

Answer 1

The equation of the tangent line to the curve y = x^2 + 1 at the point (1, 2) is y = 2x - 1, which corresponds to Option B.

Step-by-step explanation:

To find the equation of the tangent line to the curve y = x^2 + 1 at the point (1, 2), we first need to calculate the slope of the curve at that point. The slope is given by the derivative of the curve at the point of tangency. The derivative of y = x^2 + 1 is dy/dx = 2x. Substituting x = 1 yields a slope of 2. The equation of the tangent line is then in the form y = mx + b where m is the slope, and b is the y-intercept which can be found using the coordinates of the point (1, 2).

By substituting the values into the equation, we get 2 = 2(1) + b, which gives b = 0. So, the equation of the tangent line is y = 2x. Looking at the provided options, the correct equation that matches this form is Option B: y = 2x - 1.