Find an equation of the tangent line to the curve at the given point y x 36 6


Introduction

In mathematics, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that just touches the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at the point x = c on the curve if lim_(x→c)(f(x)-f(c))/(x-c) exists and is equal to f ‘(c), where f ‘(c) denotes the derivative of f at the point x = c.

What is an equation of a tangent line?

The equation of a tangent line is the equation of a line that just barely touches the curve at a given point. In other words, it is the equation of a line that has the same slope as the curve at that point.

How to find an equation of the tangent line to the curve at the given point


There are a few things that you need to know in order to find an equation of the tangent line to the curve at the given point. First, you need to know what a derivative is and how to take derivatives. Second, you need to be able to use the definition of a derivative to find the equation of the tangent line.

The derivative of a function at a certain point is the slope of the tangent line to the curve at that point. You can use this information to find an equation of the tangent line.

First, you need to take the derivative of the function. Then, you need to plug in the x and y values from the given point into the equation for the derivative. This will give you the slope of the tangent line. Once you have the slope, you can use any point on the line (including the given point) to write an equation for the line in slope-intercept form.

Conclusion

At the point (36,6), the tangent line to the curve has an equation of y = -3x + 24.


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