Question

Find the equation of the tangent at f(x) at x=0

Answer 1

Given:

The function

`f(x)=(2x)/(x^2+1)`

Required:

Find the equation of the tangent at f(x) at x=0.

Step-by-step explanation:

The slope of f(x),

`f^(\prime)(x)=(2(-x^2+1))/((x^2+1)^2)`

Now, the slope of function at x = 0 is f'(x) = 2.

The line with slope m = 2 and passing through (0, 0).

`f(x)=2x`

Answer:

Equation of tangent of the function at x = 0, f(x) = 2x.