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sashashow
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Find the equation of the line tangent to the graph of y=x^2 at the point (1/2,1/4)
and how to find that?
and how to find that?
The equation of the line tangent to a graph is used to determine the slope of the curve at a particular point. This allows us to understand the behavior of the graph at that point and make predictions about its future behavior.
The equation of the line tangent to a graph can be determined by finding the derivative of the function at the point of interest and substituting the x value into the derivative. This will give the slope of the tangent line. Then, using the point-slope form of a line, the equation can be written as y - y1 = m(x - x1), where (x1, y1) is the point of interest and m is the slope.
Yes, the equation of the line tangent can be found for any type of graph, including linear, quadratic, exponential, and trigonometric functions. However, for some functions, the derivative may not exist at certain points, making it impossible to find the equation of the tangent line at those points.
Yes, the equation of the tangent line is unique for a given point on a graph. This is because the slope of the tangent line at a point is determined by the derivative of the function at that point, which is a unique value.
The equation of the tangent line is related to the original function in that it represents the instantaneous rate of change of the function at a specific point. This means that the tangent line and the original function will intersect at that point, and the slope of the tangent line will be equal to the slope of the original function at that point.