Let f be a function twice-differentiable function defined on [0, 1] such that f(0)=0, f′(0)=0, and f(1)=0.
(a) Explain why there is a point c1 in (0,1) such that f′(c1) = 0.
(b) Explain why there is a point c2 in (0,c1) such that f′′(c2) = 0.
If you use a major theorem, then cite the theorem...
Let f(x) = \sqrt{x}
Assume that g is function such that
(i) g(c)= c+m(x-1)
(ii) f(1) = g(1), and
(iii) \lim_{{x}\to{1}}\frac{f(x)-g(x)}{x-1}
Answer the following questions. Show all of your work, and explain your reasoning.
(a) What are the constants c and m?
(b) How does g compare with the...