Answer

• f(x) = x² + 1, a = 1 We need a point and a slope. Since a = 1 and f(1) = 2, the point we want is (1,2). We found earlier that f'(1) = 2. We want a line

y = mx + b

whose slope is f'(1) = 2, so

y = 2x + b.

We want the point (1,2) to be on the line, so

2 = 2(1) + b.

Solving, we find b = 0 so the equation of the tangent line is

y = 2x.

We can check this with a picture: