- #1
mtayab1994
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Homework Statement
1) Let f be a function differentiable two times on the open interval I and a and b two numbers in I
Prove that: [tex]\exists c\in]a,b[:\frac{f(b)-f(a)}{b-a}=f'(a)+\frac{b+a}{c}f''(c)[/tex]
2) Let f be a function differentiable three times on the open interval I and a and b two numbers in I.
Prove that: [tex]\exists c\in]a,b[:f(b)=f(a)+(b-a)f'(a)+\frac{(b-a)^{2}}{2}f''(a)+\frac{b-a}{2}f'''(c)[/tex]
The Attempt at a Solution
Any tips on how to start please. Thank you in advance.