Question

If f(3) = 2 and f'(3) = -4 , find an equation of the tangent line when x = 3.

A. y = 2(x - 3) – 4
B. y = -4(x – 3) + 2
C. y = -4(x + 3) + 2
D. y = -4(x - 2) - 3

Answer 1

Answer: (y-4) = -2(x-3)

Explanation:

(y-y1) = m(x-x1)

y1 = 4

x1 = 3

m = -2

Answer 2

B

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

f'(3) = - 4 ← is the slope of the line at x = 3

and f(3) = 2 is the point (3, 2 ) thus

y - 2 = - 4(x - 3) ← add 2 to both sides

y = - 4(x - 3) + 2 → B