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