Question

Find the equation of the tangent line to the curve at the point.

A) Use the point-slope form
B) Apply the implicit differentiation
C) Employ the parametric form
D) Use the normal vector

Answer 1

To find the equation of the tangent line to a curve at a given point, use the point-slope form and then convert it to slope-intercept form.

Step-by-step explanation:

To find the equation of the tangent line to the curve at a given point, we can use the point-slope form. This involves finding the slope of the curve at that point, and then using the slope-intercept form of a line to find the equation of the tangent. Here are the steps to follow:

1. Determine the point at which you want to find the tangent line.
2. Find the slope of the curve at that point by taking the derivative or using implicit differentiation.
3. Use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the curve at that point.
4. Simplify the equation to the slope-intercept form, y = mx + b, where b is the y-intercept.