# What is the equation of the tangent line of #f(x)=3x^2# at #x=1#?

##### 2 Answers

#### Explanation:

The first objective is to find the slope of the tangent line to the curve of

Now we use the point-slope form of a line to find the tangent line equation:

We're given

#### Explanation:

We know that the function and it's tangent have the same gradient, so at

To get the gradient function of a function we know it is merely the first derivative

So now we want to find on our gradient function what the actual gradient will be at one

So as the tangent is a straight line the formula for it is

So as the two gradients are equal

Now all we have to find out is the y-intercept to do this we have to substiute a co-ordinate from the tangent in. We know that the tangent touches the function when

So we can use that co-ordinate pair from the original function

Substitue that into the tangent equation to fine c