Drag the red marker along the x axis to move the point and tangent line. Choose among polynomial, trigonometric, and logarithmic functions.
Drag the red marker along the x axis to move the point and tangent line. Choose among polynomial, trigonometric, and logarithmic functions.
This Demonstration illustrates the connection between a function and its derivative on two separate graphs. The green vertical bars indicate the value of the rate of change at the point of tangency.
This Demonstration shows the instantaneous rate of change for different x values for polynomial functions of degree 2, 3, or 4, an exponential function, and a logistic function.
Calculate the payment for a loan with given amount, interest, amortization period, and number of payments during one year. (All amounts are rounded to the nearest euro.) Also see the decomposition of the payments into interest and principal repayment parts over the years.
Typically, American mortgage lenders will offer potential borrowers a menu of loans, each of which bears an interest rate and an extra amount of "interest" that the borrower must pay at the inception of the loan. This extra prepaid interest is generally referred to as "points" and is computed as a stated fraction of the initial loan balance. The menu generally permits the borrower to "buy down" the interest rate by paying points. If the borrower thinks he or she will hold the underlying real estate for a long period, it is often a good idea to pay points. On the other hand, if the borrower thinks he or she is likely to sell the underlying real estate in the near future, points are often not a good idea.
Drag the points to change the graph of the polynomial and watch the derivative change accordingly. Nice choices will let the graph of the derivative stay within the given window.
Drag the red marker along the x axis to move the point. Choose among polynomials of degree 2, 3, 4, or 5. Check the boxes to see the tangent line and the derivative graphs.