2. Suppose that the tangent line to the graph of 𝑦 = 𝑓(𝑥) at 𝑥 = 3 passes through the points (−2,3) and (4, −1).

Question

a. Find 𝑓 ′ (3).

b. Find 𝑓(3)

c. Find the equation of the tangent line to 𝑦 = 𝑓(𝑥) at 𝑥 = 3

Answer 1

Slope of the tangent = (3+1)/(-2-4) = -2/3 and this is the value of f'(3).

The tangent line is -2/3 = (y-3)/(x+2) => y = (-2/3)x +5 and at x=3, y= -1/3; this is the value of f(3)