How do I find the tangent line of #y=x^2# at its vertex?
Let's start by finding the vertex. Then we find the derivative of the function using the x value of the vertex. Lastly, we use the slope intercept formula and the value found for the derivative to create the equation for the tangent line.
We can use the expressions
Substitute in the x value of the vertex, which is 0
Find the equation for the Tangent line:
Substitute in the slope/derivative
Solve for b, which is also known as the y-intercept
Now that we know the value of