7. Suppose that I is continuous on a closed, bounded interval [a, b]. (a) If I is...
Question:
7. Suppose that I is continuous on a closed, bounded interval [a, b].
(a) If I is differentiable on
(a,
b) and I'(x) 2: co> 0 for all x E
(a, b), prove that
(I-I)' exists and is bounded on (I(a), I(b)).
(b) If I is continuously differentiable on
(a,
b) and I'(xo) =I- 0 for some Xo E
(a, b), prove that there are intervals I and J such that I is 1-1 from I onto J and 1-1 is continuously differentiable on J.
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