Question

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

Answer 1

Given:

The function

$f(x)=\frac{2x}{x^2+1}$

Required:

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

Explanation:

The slope of f(x),

$f^{\prime}(x)=\frac{2(-x^2+1)}{(x^2+1)^2}$

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.