VIDEO: Establishing a tangent equation

Tangent and tangent equation

A tangent is a straight line that touches the function under consideration at a certain point and the slope of which is exactly the same as the slope of the function at this point.

• No matter how difficult your function is, you can use the tangent to approximate the function in a small neighborhood around the point. This procedure is also called linearization. The smaller you choose this environment, the closer this approximation will of course be.
• As you have already learned, the tangent is a straight line. It can therefore be given by the general form y = mx + c. The letter m stands for the slope, while c describes the y-axis intercept of the straight line. These two values ​​are still unknown, but can be determined using the function and a point.
• Once you have successfully determined these parameters, you can set up the tangent equation.

Establishing the equation

• Suppose you have the equation of a function through f (x) = x³ + 2 given. The point P (1 | 3) lies on the curve, as you can easily determine with a point test: f (1) = 1³ + 2 = 3.
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Function - calculation of b

The constant "b" is to be calculated for a function. It can only be ...

• Now you want to set up the tangent equation of the function at this point. The slope of the tangent corresponds to the slope of the function at this point, i.e. the first derivative there. m = f '(1) = 3 (1)² = 3.
• In the following you only have to determine the y-axis intercept of the tangent. Now you know that the point P (1 | 3) lies on the tangent. So do a point test with P and substitute m. 3 = 3 * 1 + c <=> c = 0, so the y-axis intercept of the tangent is 0.
• The tangent equation is t: y = 3x.
• Of course, you can also choose other points of the function. Of course, you will then also receive a different tangent.

You see, it is not difficult to set up the tangent equation. Practice this on two more examples and you will surely master it.