How to use implicit differentiation to find an equation of the tangent line

In this tutorial learn how to use implicit differentiation to find an equation of the tangent linegiven point of tangency. We then verify the solution using the GRAPH, WINDOW, CALC, dy/dx and TRACE features of the TI-84C.

1) If only the x value is given we should first find the point of tangency by inputting that x value into the function.

2) Calculate the first derivative of the function. This expression represents the slope of the tangent line.

3) Input the x value into the first derivative to get the numerical value of the first derivative (slope).

4a) Use the point slope formula to find the equation of the tangent line.

y-y1=m(x-x1), where the point of tangency is (x1,y1) and the slope is m.

4b) Substitute in the values for x1, y1, and m.

5) Verify your results using the Texas Instrument Graphing Calculator. TI-84, TI-84 Plus, TI-84 C

You have just found the equation of the line tangent to the function at the specified x value.