# How do you find the equation of the tangent and normal line to the curve #y=e^x# at x=0?

##### 1 Answer

Tangent Equation:

Normal Equation:

#### Explanation:

The gradient of the tangent to a curve at any particular point is given by the derivative of the curve at that point. The normal is perpendicular to the tangent and so the product of their gradients is

so If

When

So the tangent passes through

Using the point/slope form

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

# \ \ :. y = x+1 #

And for the normal:

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

# \ \ :. y = -x+1 #

We can confirm these result graphically:

graph{(y-e^x)(y-x-1)(y+x-1)=0 [-6, 6, -5, 5]}