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Magang

 Explaining real number system and plane coordinate

Determining the solution of inequalities

Determining the solution of the absolute value

Determining the functions

Determining the domain of the functions

Graphing/sketching rational functions

Determining exponential and logarithm functions

Solving arithmetic operations of function and determining its domain

Solving arithmetic operations of function and determining its domain

Determining the limit of functions

Determining continuity of functions

Determining the derivative of functions using the concept of limit

Determining the derivative of functions using product rule and quotient rule

Determining the derivative of functions using the chain rule

Solving problems related to the derivative of exponential, logarithmic, and trigonometric functions

Determining implicit differentiation

Determining high order derivatives

Determining the maxima and minima of the functions using its derivatives.

Determining the increasing/decreasing of the functions using its derivatives.

Determining the concavity of the functions using its second derivatives.

Determining the solution of problems related to optimization of functions

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 4.10 TENSION SPLINES Splines are a wonderful tool for approximation, but they can still exhibit some poor behavior. Consider the data set plotted in Fig. 4.25. Obviously, this represents a function with a severe jump near x — 0.5, but there is no sign of oscillatory behavior. However, a B-spline representation of this data (Fig. 4.26) shows small wiggles on either side of a sharp front. This is fundamentally an artifact of the steep gradient in the data, but in other contexts a spline fit can display behavior that does not match the "sense" of the data. One way to avoid the problem is the notion of a taut spline or tension spline, an idea that appears to have been first published by Schweikert [17], but which also owes a lot to the work of A. K. Cline [4]; we relied heavily on a short paper of Marusic and Rogina [12] in our presentation here. Imagine that the curve in Fig 4.26 is a piece of string that is constrained to pass through small loops at the data points. If we were...
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