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4. (a) Assume a function h is differentiable at some point to. Is it true that...


4. (a) Assume a function h is differentiable at some point to. Is it true that h is continuous on some open-neighbourhood of
4. (a) Assume a function h is differentiable at some point to. Is it true that h is continuous on some open-neighbourhood of xo? Provide either a proof or a counterexample. (b) Let f be twice differentiable on R and assume that f" is continuous. Show that for all x ER S(x) = S(0) + s°C)x + [ (x - 1))"(dt. (C) Deduce that for any twice continuously differentiable function f on R and any positive x > 0, x € R, there exists some c € (0, 2) such that 2.r - 2t .22 -f"(t) dt
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must follow the (a) As function his differentiable, so, in defination of differentiation - Let his function of n {hcus} het nNow Ginen f(n): f(0) floont Ścm-4) fC4) dx ufco) of (o)} flo) + f(o)n Sofens f(u) So, LUS: RASI LHS Left Hand Side RUS: R

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