calculus problem?

Question

Lef f be a differentiable function such that f(3)=2 and f'(3)=5. If the tangent line to the graph of f at x=3 is used to find an approximantion to a zero of f, that approximation is
a) 0.4
b) 0.5
c) 2.6
d) 3.4
e) 5.5

Answer 1

the equation of the tangent function is, with point (3, 2) and slope 5,

5(x-3) = y-2
y = 5x-13
at a zero, y = 0
0 = 5x-13
x = 13/5 = 2.6 choice (C)

Answer 2

I assume you are learning about the Newton-Raphson Method. The general equation looks like this

x1 = x0 - f(x0)/f'(x0)

If x0 = 3,

x1 = 3 - 2/5 = 2.6

Therefore, the answer is C.