How to solve function graph and the tangent

The task of drawing up the equation of the tangent to the graphics functions is reduced to the necessity of making a selection of the many direct to those that can satisfy specified requirements. All this straight can be defined either by points or angular factor. In order to solve graph the function and the tangent, you need to perform certain actions.

Instruction

1. Read carefully the task of writing the equation of a tangent. As a rule, there is a certain equation graph functionsexpressed in x and y and the coordinates of one point tangent.
2. Plot the function in the x and y coordinates. To do this, make a table of the ratio of equity y at a given x value. If the schedule function is nonlinear, then to build will need at least five coordinates. Draw coordinate axes and the graph of the function. Put also the point, which is specified in the problem statement.
3. Find the value of the abscissa of the touch point, which is marked with the letter "a". If it coincides with the given point tangent, then "a" will be equal to its x-coordinate. Determine the value of the function f(a), substituting in the equation of the function value of the abscissa.
4. Determine the first derivative equation of the function f'(x) and substitute in it the value of the point "a".
5. Take the General equation of the tangent, which is defined as y = f(a) = f (a)(x – a), and substitute into it the values of a, f(a), f '(a). The result will be found the solution of functions graph and a tangent.
6. Let's solve the problem another way, if the given tangent point does not coincide with the point of tangency. In this case, the equation of the tangent instead of numbers to substitute the letter "a". After that, instead of letters "x" and "y" substitute the coordinate value of the set point. Solve the resulting equation in which the letter "a" is unknown. Put the obtained value in the equation of the tangent.
7. Write down the equation of the tangent with the letter "a" if the task is set to the equation of the function and the equation of the parallel line for the desired tangent. After that you need to find the derivative of the function is parallel to the line to determine the y-coordinate of the point "a". Substitute the appropriate value for the equation of the tangent and the solve function.