How to plot the graph of a function
How to plot the graph of a function
If the graph of the derivative has clearly expressed signs, it is possible to make assumptions about the behavior of the antiderivative. When constructing a function graph, check the conclusions drawn on the characteristic points.
Instructions
1
If the graph of the derivative is straight, parallelaxis, then its equation is Y "= k, then the required function Y = k * x If the graph of the derivative is a straight line passing at an angle to the numerical axes, then the graph of the function is a parabola.If the derivative graph is similar to a hyperbola, his research suggests that the antiderivative is a function of the natural logarithm.If the graph of the derivative is a sinusoid, then the function is the cosine of the argument.
2
If the plot of the derivative is a straight line, then its equationin general form, we can write Y "= k * x + b To determine the coefficient k for the variable x, draw a straight line parallel to the given graph through the origin: Remove the coordinates x and y of an arbitrary point from this auxiliary graph and calculate k = y / x. k set in the direction of the derivative graph - if the graph rises with increasing value of the argument, hence k> 0. The value of the free term b is equal to the value of Y "at x = 0.
3
Determine the formula of the function from the compiledthe equation of the derivative: Y = k / 2 * x² + bx + c The free term can not be found from the plot of the derivative. The position of the function graph along the Y axis is not fixed. By points, plot the resulting function - the parabola. The branches of the parabola are directed upwards for k> 0 and downwards for k <0.
4
Graph of the derivative of the exponential functioncoincides with the graph of the function itself, since in the differentiation the exponential function does not change. The control point of the graph has coordinates (0, 1), because any number of zero power is equal to one.
5
If the graph of the derivative is a hyperbola with branches inthe first and third quarters of the coordinate axis, then the equation of the derivative is Yn = 1 / x, so the antiderivative will be a function of the natural logarithm.The control points when constructing the graph of the function (1,0) and (e, 1).
