step function

f (x) = [x] = greatest integer less than or equal to x [x] = n, where n is an integer such tha..

Show that the function is continuous in the given interval. Some known standard functions which are continuous, can be mentioned directl..

Show the function f (x) is continuous on the closed interval [a, b..

For a differentiable function f (x), find f '(x). Equate it to zero. Solve the equation f '(x) = 0 to get the Critical values of f (x..

Find f '(x) and examine if it is defined at every point on the open interval (a, b). If f '(x) is defined for all x (a, b), then the function is differentiabl..

Identify the corner point at which the value of the objective function is maximum (or minimum depending on the LPP) The co-ordinates of this vertex is the optimal solution and the value of Z is the optimal val..

We have the following conditions on the variables x and y. a) Sum of the numbers is atleast 15 i.e., x + y 15 b) Difference of the numbers is at most 7 i.e., x - y 7 c) Since the x and y should be positive, we have two more conditions x > 0, y > 0 We call Z as objective function..

If y = f(x) is differentiable then is called the first order derivative of y = f(x) if is further differentiable the is called the second order derivative of f(x).Derivatives of standard functions ..

(x) of x under f is called the value of 'f ' at x. Types of Function and their Graphs: Constant function, Identity function, Polynomial function, Modulus function, Square root function, Greatest integer function or Step..

. groups with elimination of H 2 O, NH 3 etc. and formation of linkages such as ester, amides etc. Even electrophilic aromatic substitution of phenols with formaldehyde forms polymers having C-C linkages. Each condensation step provides a bi or poly functionalized product and th..