Question

Proof involving the MVT. Question in comments

Answer 1

Question 6 involves the MVT:
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/exam-2/materials-for-exam-2/MIT18_01SCF10_exam2.pdf
Answer:
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/exam-2/materials-for-exam-2/MIT18_01SCF10_exam2sol.pdf

The MVT states that:
\[{f(b)-f(a)}/{b-a} = f'(c)\]

However, it looks to me like we are equating f(b)-f(a) with f'(c). Where did the /b-a part go in this proof

Answer 2

Prove that
\[ \sqrt{1 +x} < 1 + {1 \over 2}x\]
is this one?

Answer 3

Yes

Answer 4

this insn't using MVT ... just show that the function is increasig for g(x) > 0 for all x>0

Answer 5

http://www.wolframalpha.com/input/?i=expand+sqrt%281%2Bx%29
the terms are alternating!! looks like i made error in previous post.

Answer 6

hmm could you maybe quickly explain how showing that is the same as showing that \[\sqrt{1+x}>1+\frac{1}{2}x\]