Finding Equations of Tangent Lines for Any Curve By Mai Tyler

On the AP Calculus exam, many students struggle with finding the equation of a tangent line to a point when given an equation of a line in the following format: f(x)= y and f’(x)=z as well as a point (x,y). Oftentimes, a chart with information regarding a function and its derivative will be given, and students must look for the necessary values to complete the problem.

The Derivative of an equation is the equation that represents all tangent lines relative to any given point on a curve. Given an equation of a graph and a point on that graph, we are able to find the derivative which will give us the slope, and therefore the equation of the tangent line.
If a point and an equation is given, the equation of the tangent line can be produced using the equation of slope-intercept form y=mx+b.

Hereare 2 examples of how to find the equation of the tangent line at a particular Point on the curve F.

No function is actually given, but the information is provided within the problem.

When given an actual Trigonometric function, we must derive our equation for slope, then refer to the Unit Circle to find the appropriate values for points on the given curve. We complete the task by computing the slope value at the given point, and then using the point and slope, we can write the equation of the tangent line at the given point on the curve, as shown in the following video.