ugg...Please help! What is the linear approximation to f(x) = 2/x at x sub 0 = 2 ?

Answer 1

The linear approximation to f(x) at x_0 is the tangent line to f(x) at x_0, whose equation is

y - y_0 = f'(x_0)(x - x_0).

Compute f'(x) = -2/x^2.
Evaluate f'(x_0) = f'(2) = -1/2.
Plug in f'(x_0) = -1/2, x_0 = 2 and y_0 = f(x_0) = 1 into the above equation.

Answer 2

The linear approximation is

y-f(2) = f'(2)(x-2), (from y-y0 = m(x-x0))

where where f'(2) is the derivative evaluated at x=2.