Examples on how to solve for the tangent lines are widely available in the textbooks. However, students cannot see these examples in the books or in the software used for taking the law exam. If they do not have a copy of them in front of them, they can look for them in the Internet. The examples are in video format so that the student can review them thoroughly.
The first example is the tangent of a curve on the x axis and the first derivative of the curve on the y axis. The tangent of a curve on the x axis is the tangent of the curve on the x-axis and also the first derivative of the curve on the y-axis. Both the variables can be plotted onto the graph. Using the quadratic formula, the area below the curve and the area above the tangent will help determine the value of the second derivative.
A second example involves the second derivative of the tangent. This involves the derivatives of the tangent on the x-axis as well as the derivatives of the tangent on the y-axis. After the student finds out the values of the derivatives, the area of the tangent will be determined. The area of the tangent is the function of the tangent on the tangent plane. Understanding the definitions of the function of the tangent will help students plot the tangent onto a tangent plane so that the function can be evaluated.
A third example will allow students to see why the tangent of a curve acts as a parabola when graphed. This allows the student to visualize why the tangent of a parabola varies as a function of the angle that it lies in. This will be important in calculus courses such as geometric calculus. The formulas for these parabola functions should be understood by students when they are taking calculus courses such as vector calculus.
The fourth set of examples in the tangent plane will deal with the quadratic formula. Students must have already learned the definition of the tangent plane and must be familiar with the quadratic formula so that they can evaluate the tangent of a parabola on the tangent plane. They will use the quadratic formula to find the derivative of the parabola along any one of its tangents.
The last set of examples in the tangent plane will cover the integral formula for the parabola. This is the most difficult section of the tangent plane to understand, but students must have a good working knowledge of algebra before proceeding. In the integration, students must find the area between the two tangent planes. Using a formula based on the integral formula for the parabola, the area between the tangent plane and the parabola is measured. This equation is then used to find the derivative of the function on the tangent plane. Students must also understand that these functions take the derivatives of the functions on the x axis, which means that they must also be linearly dependent.
Understanding calculus curvature is important for those preparing to take calculus courses such as geometric or calculus. Understanding how to plot tangent planes, finding the integral formula for a parabola, and understanding how to evaluate geometric functions on the x axis are just a few of the things that students will learn when they take a calculus course in college. Students should understand that the concepts of calculus will not be the same as algebra or high school mathematics. However, they can use basic math techniques, such as subtraction, addition, and multiplication, to develop a solid understanding of the concepts of calculus.
