Example Give an equation of the tangent line to the curve f(x) = 1/2x^ 2 − 2x + 7/2 at the point (1, 2)

Answer 1

f'(x) = x - 2. Slope of tangent line: m = f'(1) = 1 - 2 = - 1.

So equetion of tangent line y = 2 -1(x - 1) = - x + 3;

Answer: y = - x + 3 is equation of tangent line.

Answer 2

Tangent = same location AND slope at a given point.

Given the point and the function, our steps are:

1) Take the derivative

2) Plug in the point's x-value to the derivative to get the slope

3) Plug in the point and slope to the point-slope formula for a line