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16 lis 2022 · A tangent line to the function \ (f (x)\) at the point \ (x = a\) is a line that just touches the graph of the function at the point in question and is “parallel” (in some way) to the graph at that point. Take a look at the graph below.
How tangent lines are a limit of secant lines, and where the derivative and rate of change fit into all this.
tangent and secant lines is greatest where the graph of f(x) is curved. If the graph of y = f(x) is sharply curved, the value of x must be very close to 0 for the secant line to be close to the tangent line.
26 wrz 2024 · The tangent line to \(f(x)\) at a is the line passing through the point \((a,f(a))\) having slope \(m_{tan}=lim_{x→a}\frac{f(x)−f(a)}{x−a}\) provided this limit exists. Equivalently, we may define the tangent line to \(f(x)\) at a to be the line passing through the point \((a,f(a))\) having slope \(m_{tan}=lim_{h→0}\frac{f(a+h)−f(a)}{h}\)
A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line. A chord is the line segment that joins two distinct points of a circle.
Let's say you wanted to find the slope of the secant line between the point (2.5, 6.25) and (3, 9)? And what if you just kept getting closer and closer and closer? Well then, the slopes of these secant lines are going to get closer and closer to the slope of the tangent line at x equals 3.
