Let y=f(x) be a differentiable function such that dy/dx = x/y and f(8) = 2. What is the approximation of f(8.1) using the line tangent to the graph of f at x=8

Question

The answer must be either

.4

2.025

2.4

6

Thankyou!

Answer 1

Equation of the tangent line to the graph of y = f(x) at the point (8,2):

y - 2 = f'(8)(x - 8)

y = (8/2)(x - 8) + 2

y = 4x - 30

f(8.1) ≈ 4(8.1) - 30 = 2.4