Compound interest. Annuities.
Derived functions.
Development of an entire function F(x + h) of the binomial (x + h).—Derivative of an entire function.—To return from the derivative to the function.
The derivative of a function of x is the limit towards which tends the ratio of the increment of the function to the increment h of the variable, in proportion as h tends towards zero.
Derivatives of trigonometric functions.
Derivatives of exponentials and of logarithms.
Rules to find the derivative of a sum, of a product, of a power, of a quotient of functions of x, the derivatives of which are known.
Of the numerical resolution of equations.
Changes experienced by an entire function f(x) when x varies in a continuous manner.—When two numbers a and b substituted in an entire function f(x) give results with contrary signs, the equation f(x) = 0 has at least one real root not comprised between a and b. This property subsists for every species of function which remains continuous for all the values of x comprised between a and b.
An algebraic equation of uneven degree has at least one real root.—An algebraic equation of even degree, whose last term is negative, has at least two real roots.