Let f(x) be defined for all x > 0 by f(x) = (In x)³-2 (In x)² + In x (a) Compute f(e²) and find the zeros of f(x). (b) Prove that f(x) defined on [e, ∞o) has an inverse function h and determine h'(2).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 3.
Let f(x) be defined for all x > 0 by
f(x) = (In x)³ - 2 (lnx)² + Inx
(a) Compute f(e²) and find the zeros of f(x).
(b) Prove that f(r) defined on [e, ∞o) has an inverse function h and determine
h' (2).
Transcribed Image Text:Problem 3. Let f(x) be defined for all x > 0 by f(x) = (In x)³ - 2 (lnx)² + Inx (a) Compute f(e²) and find the zeros of f(x). (b) Prove that f(r) defined on [e, ∞o) has an inverse function h and determine h' (2).
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