# Hi. I don't quite get this: At the point where the function f(x) = e^x intersects the y-axis the tangent is drawn. Find the x-coordinate of the intercept of this tangent with the x-axis. ?

##### 1 Answer

#### Explanation:

The given function is

A tangent is said to be drawn at the point where

Let's find this

The

So, a tangent is drawn at the point where

Now, we need to find an equation for the tangent drawn at this point.

Let's differentiate

The derivative of

Now, we need to find the gradient of the tangent at

Let's substitute

So, the gradient of the tangent is

We can now write an equation for the tangent drawn at

Finally, we are required to find the

So let's the equation of the tangent equal to zero:

Therefore, the tangent intersects the