initial value problems calculus

Because of these condition, the 2 n d order differential equation y''= 2 has particular solution x 2 + x + 2. The values f (0) = 2 and f '(0) = 1 are called initial values. The problem of finding the solution of a differential equation that satisfies these pr..

We can take the value of f at a (i.e., f(a)) as first estimate for average value of the function. Divide [a, b] into two equal parts such that then the second estimate of the average value of the function can be taken as second estimate of the average value o..

Let f be real valued function in [a,b] such that, 1. f is continuous in [a,b]. 2. f is differentiable in (a,b). ..

Rolle's Theorem - Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

Let f (x) be a real valued function with its domain D. (i) f(x) is said to have absolute maximum value at x = a if f(a) f(x) for all x D. (ii) f(x) is said to have absolute minimum value at x = a if f(a) f(x) for all x D. The following points are to be n..

Let f (x) be the real valued differentiable functio..

Take the maximum and minimum values of f out of the values calculated in step 3. These will be the absolute maximum or absolute minimum values..

The value of c obtained need not be uniqu..

The value of c need not be uniqu..

Let f be a continuous function on an interval I = [a, b]. Then, f has the absolute maximum value and f attains it at least once in I. Also, f has the absolute minimum value and attains it at least once in ..