Question

Find the tangent line to the graph of f(x)=x at point (0,0)

Answer 1

Given:

The function is

$f(x)=x$

To find:

The tangent line to the graph of f(x)=x at point (0,0).

Solution:

We have,

$f(x)=x$

It is a linear function because the highest power of the variable is 1.

We know that the tangent line to a linear function at any point is the line itself.

Derivative of given function is

$f'(x)=1$

So, slope of the tangent line is 1. It is given table the tangent line passes through the point (0,0). The equation of tangent line is

$y-0=1(x-0)$

$y=x$

Therefore, the tangent line to the graph of f(x)=x at point (0,0) is y=x.