[See Solution] Prove that t* = + (10) To do this, reason by contradiction as follows: Assume t* < + , Recall also that t* > 0. Note that f(z) > 1 for all
Question: Prove that
t* = +
(10)
To do this, reason by contradiction as follows: Assume t* < +
, Recall also that t* > 0. Note that f(z) > 1 for all z
] 0, t* [ (Why??). Use (9) and (1) and the Mean Value Theorem to obtain a contradiction, Conclude that (10) holds, and deduce from there that
f(t) > 1 for all t > 0 (11)
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(Step-by-Step) Recall that P o (t) = 1 for every t 0. Use this fact,
![[Steps Shown] Consider a continuous, positive function](/images/solutions/MC-solution-library-42423.jpg "[Steps Shown] Consider a continuous, positive function f: . The")
[Steps Shown] Consider a continuous, positive function f: . The
![[Solution] Use (12), along with the Intermediate](/images/solutions/MC-solution-library-42424.jpg "[Solution] Use (12), along with the Intermediate Value Theorem")
[Solution] Use (12), along with the Intermediate Value Theorem
![[Solution] Consider now the function A(x) defined](/images/solutions/MC-solution-library-42425.jpg "[Solution] Consider now the function A(x) defined as the area")
[Solution] Consider now the function A(x) defined as the area
(See Solution) Use Part c to prove that A’(x) = f(x) (15) To do this,
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