Lecture II. The elements of higher mathematics . The derivative of function. Lecture question s. Function R epresent ation o f a function Function derivative G eometric interpretation of function derivative Some differentiation rule s
The elements of higher mathematics .
The derivative of function
A relationship between two variables, typically x and y, is called a function if there is a rule that assigns to each value of x one and only one value of y.
When that is the case, we say that y is a function of argument of x.
There are many ways to represent or visualize functions: a function may be described by a formula, by a plot or graph, by an algorithm that computes it, by arrows between objects, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (for example, inverse functions). In applied disciplines, functions are frequently specified by tables of values or by formulas. The equation y = ƒ(x) is viewed as a functional relationship between dependent and independent variables.
of the second derivative:
of a higher order derivatives:
At B and R points, where a function is increasing, the tangent makes an acute angle with the axis of x, hence the slope is positive. At M and Q points, where a function is decreasing, the tangent makes an obtuse angle with the axis of x, therefore the slope is negative.C and P points are maxima. N point is a minimum.
Thank you for your attention !