Question

Can The Equation Of A Tangent Line Be Found For A Whole Function? Explain Your Reasoning.

Answer 1

The equation of a tangent line can be found for a whole function by following the steps of finding the derivative, substituting the desired point, and using the point-slope form of the line equation.

Step-by-step explanation:

The equation of a tangent line can be found for a whole function. In calculus, the slope of a curve at a point is equal to the slope of the tangent line at that point. To find the equation of the tangent line, you need to find the slope of the curve at the desired point and then use the point-slope form of the equation of a line.

For example, if you have a function f(x) and want to find the tangent line at x = a, follow these steps:

1. Find the derivative of the function f'(x).
2. Substitute x = a into f'(x) to find the slope of the curve at x = a.
3. Use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the curve at x = a and m is the slope found in step 2.