Question

How to find tangent line at a point?

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

Answer 1

To find the tangent line at a point on a curve, you can use the point-slope form. Steps are: Identify the point, calculate the slope using the derivative, and use point-slope form to find the equation.

Step-by-step explanation:

To find the tangent line at a point on a curve, you can use the point-slope form. Here are the steps:

1. Identify the point at which you want to find the tangent line.
2. Calculate the slope of the curve at that point using the derivative of the function.
3. Use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope, to find the equation of the tangent line.

For example, if you have the curve y = x^2 and you want to find the tangent line at the point (2, 4), you would calculate the derivative dy/dx = 2x and find that it equals 4 at x = 2. Then, using the point-slope form, the equation of the tangent line is y - 4 = 4(x - 2).