Prove the following variant Theorem 4.14. Suppose f [a, b] → R is -1,1. If f is differentiable at c = [a, b], f'(c) ‡ 0, and f-¹ is continuous at d = f(c), then f-¹ is differentiable at d and (f-¹')'(d) = = 1 f'(c)

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Chapter2: Second-order Linear Odes
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Prove the following variant Theorem 4.14. Suppose f: [a, b] → R is −1,1. If f is
differentiable at c € [a, b], f'(c) ‡ 0, and f-¹ is continuous at d f(c), then f-¹ is
differentiable at d and
(ƒ˜¹)'(d)
1
f'(c)
Transcribed Image Text:Prove the following variant Theorem 4.14. Suppose f: [a, b] → R is −1,1. If f is differentiable at c € [a, b], f'(c) ‡ 0, and f-¹ is continuous at d f(c), then f-¹ is differentiable at d and (ƒ˜¹)'(d) 1 f'(c)
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