How to find the x-coordinate of the touch point

Draw on a sheet in the box of axes x and y. Examine the given equation for the graph of a function. If it is linear, it is enough to know two values for the parameter d for any x, and then build the found point on the coordinate axis and connect them with a straight line. If the graph is nonlinear, then make a table of the dependence from x and pick up at least five points to plot.

Plot the function and put it on a coordinate axis specified point tangent. If it coincides with a function, its x-coordinate is equal to the letter a, which is denoted by the x coordinate of the touch point.

Determine the value of the abscissa of the touch point when the specified point is not a tangent coincides with the graph of the function. Specify a third parameter with the letter "a".

Write down the equation of the function f(a). To do this in the original equation instead of x and substitute. Find the derivative of the function f(x) and f(a). Substitute required data in the General equation of the tangent, which has the form: y = f(a) + f '(a)(x – a). The result is an equation that consists of three unknown parameters.

Substitute in place of x and y coordinates of the given point through which the tangent passes. Then find the solution of this equation for all and. If it is a square, there will be two values of the abscissa of the touch point. This means that the tangent line passes twice near the graph of a function.

Draw a graph of the given function and is parallel to the line defined according to the problem. In this case, you must also specify the unknown parameter a and substitute it into the equation f(a). Paranaita the derivative f(a) to the derivative of the equation of a parallel line. This action comes from the condition of parallelism of two functions. Find the roots of the resulting equation, which will be the abscissa of the touch point.