 | J. V. Deshpande - 2004 - 362 σελίδες
...Theorem can be applied. Define F(x) = (W - /(°))g(*) - (9(b) - 9(a))f(x) for a < x < b. This function F is continuous on [a, b] and differentiable on (a, b) and F(b) = (f(b)-f(a))g(b)-(g(b)-g(a))f(b) = f(b)g(a)-f(a)g(b) = F(a). as is easily verified. Hence, by... | |
 | David M. Bressoud - 2007 - 352 σελίδες
...function defined as /' on (a, b), /|(a) at x - a, and f'_(b) at x - b. Exercises 3.5.1. Prove that if F is continuous on [a, b] and differentiable on (a, b) and if F'(x) is not zero for any x strictly between a and b, then F(b) ^ F(a). 3.5.2. Show that the approximation... | |
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Suppose that f is continuous on [a, b] and differentiable on (a, b), and that /(a) = f(b). 