Yahoo Answers: Answers and Comments for AP Calculus Derivatives of Inverse Functions? [Mathematics]
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From Claire
enUS
Tue, 24 Oct 2017 18:34:11 +0000
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Yahoo Answers: Answers and Comments for AP Calculus Derivatives of Inverse Functions? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20171024183411AAdaCgX
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From kb: Observe that f'(x) = (1/27)(5x^4 + 6x^2) i...
https://answers.yahoo.com/question/index?qid=20171024183411AAdaCgX
https://answers.yahoo.com/question/index?qid=20171024183411AAdaCgX
Tue, 24 Oct 2017 19:56:11 +0000
Observe that f'(x) = (1/27)(5x^4 + 6x^2) is nondecreasing. Hence, f has an inverse.
When a (= y) = 11, we find that x = 3, because f(3) = 11.
So, the Inverse Function Theorem yields
(f^(1))'(11) = 1/f'(x) {at x = 3}
....................= 1/[(1/27)(5x^4 + 6x^2)] {at x = 3}
....................= 27/(x^2 * (5x^2 + 6)) {at x = 3}
....................= 27/(9 * (45 + 6))
....................= 1/17.
I hope this helps!