What is the first step in finding the equation of a line tangent to a function?

The correct approach to finding the equation of a line tangent to a function starts with taking the derivative of that function. The derivative provides the slope of the tangent line at any given point on the curve. By calculating the derivative, you can evaluate it at the specific point of tangency to determine the slope of the tangent line.

To find the equation of the tangent line, you will need both a point on the curve and the slope at that point. After finding the derivative, you can then substitute the x-coordinate of the point of tangency into the derivative to get the slope. This slope, along with the coordinates of the point on the function, will allow you to use the point-slope form of a line to write the equation of the tangent line.

While the other choices may seem relevant in different contexts, they do not address the foundational step necessary for deriving the tangent line. Evaluating the function at the point of tangency is important but comes after determining the slope from the derivative. The slope-intercept form is a way to express the line once you have both the slope and the point, rather than being a first step. Calculating the area under the curve pertains to integral calculus, which is not necessary for finding a tangent line.