How do you find the equation of a line tangent to the function #y=x^2(x-2)^3# at x=1?
The equation is
To find the equation of a line, you need three pieces: the slope, an
The first step is to find the derivative. This will give us important information about the slope of the tangent. We will use the chain rule to find the derivative.
The derivative tells us the points what the slope of the original function looks like. We want to know the slope at this particular point,
Now, we have a slope and an
Therefore, our slope is
Finally, we can construct the equation of the tangent.